Link prediction is to complete the missing links in the network or to predict the generation of new links according to the current network structure information, which is very important for mining and analyzing the evolution of the network such for construction and analysis of logical architecture in 6G network. Link prediction algorithms based on node similarity need predefined similarity functions, which is highly hypothetical and only applies to specific network structures without generality. To solve this problem, this paper proposes a link prediction algorithm based on the subgraph of the target node pair. In order to automatically learn the graph structure characteristics, the algorithm firstly extracts the h-hop subgraph of the target node pair, and then predicts whether the target node pair will be linked according to the subgraph. Experiments on seven real data sets show that the link prediction algorithm based on target node pair subgraph is suitable for various network structures and superior to other link prediction algorithms.

A growing area in neurosciences is focused on the modeling and analysis the complex system of connections in neural systems, i.e. the connectome. Here we focus on the representation of connectomes by using graph theory formalisms. The human brain connectomes are usually derived from neuroimages; the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network - this process is referred to as parcellation. Recently, it has been proposed to perform atlas-free random brain parcellation into nodes and align brains in the network space instead of the anatomical image space to define network nodes of individual brain networks. In the network domain, the question of comparison of the structure of networks arises. Such question is tackled by modeling the comparison of brain network as a network alignment (NA) problem. In this paper, we first defined the NA problem formally, then we applied three existing state of the art of multiple alignment algorithms (MNA) on diffusion MRI-derived brain networks and we compared the performances. The results confirm that MNA algorithms may be applied in cases of atlas-free parcellation for a fully network-driven comparison of connectomes.

Convolutional neural networks (CNN) have attracted much attention as a commonly used method for hyperspectral image (HSI) classification in recent years, however, CNNs can only be applied to Euclidean data and have limitations in dealing with relationships due to the limitations of local feature extraction. However, each pixel of a hyperspectral image contains a set of spectral bands that are correlated and interact with each other, and the methods used to process Euclidean data cannot effectively obtain these correlations. In contrast, the graph convolutional network (GCN) can be used in non-Euclidean data, but usually leads to oversmoothing and ignoring local detail features due to the need for superpixel segmentation processing to reduce computational effort. To overcome the above problems, we constructed a network a fusion network based on GCN and CNN, which contains two branches: a graph convolutional network based on superpixel segmentation and a convolutional network with added attention mechanism. The graph convolu-tional branch can extract the structural features and capture the relationships between the nodes, and the convolutional branch can extract the detailed features in the local fine region. Owing to the fact that the features extracted from the two branches are different, the classification performance can be improved by fusing the complementary features extracted from the two branches. To vali-date the proposed algorithm, experiments were conducted on three widely used datasets, namely Indian Pines, Pavia University, and Salinas, and the overall accuracy of 98.78% was obtained in the Indian Pines dataset, and the overall accuracy of 98.99% and 98.69% was obtained in the other two datasets. The results showed that the proposed fusion network can obtain richer features and achieve high classification accuracy.

There is a considerable amount of research in online social networks, most of which focuses on the structural analysis of social graphs. The interpersonal relationships of social networks, especially friend circle, can solve the cold start and sparsity problems, and through the relationship between social networks can effectively recommend users' favorite items (items), such as music , videos, brands/products, preferred tags, location, services, etc. User relationships in social networks are diverse and there are many different perspectives on different social networks. Associations among users can form multi-layered composite networks, and multi-layered social networks present new challenges and opportunities. Different relationships can influence users' preferences to different degrees, which in turn affects their behavior. Therefore, fusing multiple social networks is an effective way to improve recommendation. Although some studies have started to address multiple social network recommendations, simple linear superposition cannot reflect the coupling and nonlinear association between multiple social networks. In this paper, we propose a graph neural network recommendation model under social relationships based on this background. We first propose to compute the 2nd order collaborative signals and their intensities directly from the neighboring matrix for updating the node embedding of the graph convolution layer. Secondly by embedding historical evaluations, various social networks constituting different dimensions, the attention integration of user preferences by different social networks is achieved, and its effectiveness and scalability are demonstrated in theoretical derivation and experimental validation. The theoretical derivation and experimental validation demonstrate its effectiveness and scalability.

With the improvement of software copyright protection awareness, code obfuscation technology plays a crucial role in protecting key code segments. As the obfuscation technology becomes more and more complex and diverse, it has spawned a large number of malware variants, which make it easy to evade the detection of anti-virus software. Malicious code detection mainly depends on binary code similarity analysis. However, the existing software analysis technologies are difficult to deal with the growing complex obfuscation technologies. To solve this problem, this paper proposes a new obfuscation-resilient program analysis method, which is based on the data flow transformation relationship of the intermediate representation and the graph network model. In our approach, we first construct the data transformation graph based on LLVM IR. Then, we design a novel intermediate language representation model based on graph networks, named DFSGraph, to learn the data flow semantics from DTG. DFSGraph can detect the similarity of obfuscated code by extracting the semantic information of program data flow without deobfuscation. Extensive experiments prove that our approach is more accurate than existing deobfuscation tools when searching for similar functions from obfuscated code.

Animal models of diseases in particular, the mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the edge directions of the graph model, a mass balance approach to lymph dynamics based on Hagen-Poiseuille equation is applied. It is the first study in which a geometric model of the murine LS has been developed and characterized in terms of its structural organization and the lymph transfer function. Our study meets the demand for quantitative mechanistic approaches in the growing field of immunoengineering to utilize or exploit the lymphatic system for immunotherapy.

Here we present a fast and highly scalable community structure preserving network module detection that recursively integrates graph sparsification and clustering. Our algorithm, called SparseClust, participated in the most recent DREAM community challenge on disease module identification, an open competition to comprehensively assess module identification methods across a wide range of biological networks.

With the deepening of the diversification and openness of financial system, financial vulnerability, as an endogenous attribute of financial system, becomes an important measurement of financial security. Based on network analysis, we introduce network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with previous network curvature analysis method, CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

With the rapid development of Internet of Things (IoT)-based near-earth remote sensing technology, the problem of network intrusion for near-earth remote sensing systems has become more complex and large-scale. Therefore, it is essential to seek an intelligent, automated, and robust network intrusion detection method. In recent years, network intrusion detection methods based on graph neural networks (GNNs) have been proposed. However, there are still some practical issues with these methods. For example, they have not taken into consideration the characteristics of near-earth remote sensing systems, the state of the nodes, and the temporal features. Therefore, this article analyzes the characteristics of existing near-earth remote sensing systems and proposes a spatio-temporal graph attention network (N-STGAT) that considers the state of nodes. The proposed network applies spatiotemporal graph neural networks to the network intrusion detection of near-earth remote sensing systems and validates the effectiveness of the proposed method on the latest flow-based dataset.

The root system plays an irreplaceable role in plant growth. Its improvement can increase crop productivity. However, such system is still mysterious for us. The underlying mechanism has not been fully uncovered. The investigation on proteins related to the root system is an important means to complete this task. In the previous time, lack of root-related proteins makes it impossible to adopt machine learning methods for designing efficient models for the discovery of novel root-related proteins. Recently, a public database on root-related proteins was set up and machine learning methods can be applied in this field. In this study, we proposed a machine learning based model, named Graph-Root, for identification of root-related proteins. The features derived from protein sequences and one network were extracted, where the former features were processed by graph convolutional neural network and multi-head attention, and the later features abstracted the linkage between proteins. These features were fed into the fully connected layer to make prediction. The 5-fold cross-validation and independent tests suggested its good performance. It also outperformed the only one previous model, SVM-Root. Furthermore, the importance of each feature type and component in the proposed model was investigated.

Drug repositioning (also called drug repurposing) is a strategy for identifying new therapeutic targets for existing drugs. This approach is of great importance in pharmacology as it is a faster and cheaper way to develop new medical treatments. In this paper, we present, to our knowledge, the first application of multiplex-heterogeneous network embedding to drug repositioning. Network embedding learns the vector representations of nodes, opening the whole machine learning toolbox for a wide variety of applications including link prediction, node labelling or clustering. So far, the application of network embedding for drug repositioning focused on heterogeneous networks. Our approach for drug repositioning is based on multiplex-heterogeneous network embedding. Such method allows the richness and complexity of multiplex and heterogeneous networks to be projected in the same vector space. In other words, multiplex-heterogeneous networks aggregate different multi-omics data in the same network representation. We validate the approach on a task of link prediction and on a case study for SARS-CoV2 drug repositioning. Experimental results show that our approach is highly robust and effective for finding new drug-target associations.

The basic challenges of this work are twofold: demonstrating the dependence between the functional and topological qualities of partition networks and finding the simplest—with respect to algorithmic complexity—network elements. The study of these problems is based on finding the solution to an appropriate antagonistic vertex game. The results of the numerical simulations of antagonistic partition games demonstrate that the winner’s graphs are “almost always” dense and hyperenergetic compared to the loser’s graphs. These observations reveal that successful evolutionary mechanisms can be realized, in principle, by the simplest objects (such as viruses).

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.

We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

A signed graph is an undirected graph such that all of its edges are labeled positive or negative. Let D be an embedding of a signed graph G in the Euclidean line. If in D for all of the vertices their positive neighbors are closer than the negative neighbors, then D is called a valid drawing of G. In this paper we show that signed trees, unicyclic graphs, and ladder graphs have a valid drawing in the Euclidean line.

The commonly-used large-scale knowledge bases have been facing challenges in open domain question answering tasks which are caused by the loose knowledge association and weak structural logic of triplet-based knowledge. To find a way out of this dilemma, this work proposes a novel metaknowledge enhanced approach for open domain question answering. We design an automatic approach to extract metaknowledge and build metaknowledge network from Wiki documents. For the purpose of representing the directional weighted graph with hierarchical and semantic features, we present an original graph encoder GE4MK to model the metaknowledge network. Then a metaknowledge enhanced graph reasoning model MEGr-Net is proposed for question answering, which aggregates both relational and neighboring interactions comparing with R-GCN and GAT. Experiments have proved the improvement of metaknowledge over main-stream triplet-based knowledge. We have found that the graph reasoning models and pre-trained language models also have influences on the metaknowledge enhanced question answering approaches.

Everyday place descriptions provide a rich source of knowledge about places and their relative locations. This research proposes a place graph model for modeling this spatial, non-spatial, and contextual knowledge from place descriptions. The model extends a prior place graph, and overcomes a number of limitations. The model is implemented using the Neo4j graph database, and a management system has also been developed that allows operations including querying, mapping, and visualizing the stored knowledge in an extended place graph. Then three experimental tasks, namely georeferencing, reasoning, and querying, are selected to demonstrate the superiority of the extended model.

The Randić index of a graph G is the sum of (dG(u)dG(v))−1/2 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease Randić index of graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs, and characterize the corresponding extremal graphs.

Ligand-based virtual screening (LBVS) is a promising approach for rapid and low-cost screening of potentially bioactive molecules in the early stage of drug discovery. Compared with traditional similarity-based machine learning methods, deep learning frameworks for LBVS can more effectively extract high-order molecule structure representations from molecular fingerprints or structures. However, the 3D conformation of a molecule largely influences its bioactivity and physical properties, and has rarely been considered in previous deep learning-based LBVS methods. Moreover, the relative bioactivity benchmark dataset is still lacking. To address these issues, we introduce a novel end-to-end deep learning architecture trained from molecular conformers for LBVS. We first extracted molecule conformers from multiple public molecular bioactivity data and consolidated them into a large-scale bioactivity benchmark dataset, which totally includes millions of endpoints and molecules corresponding to 954 targets. Then, we devised a deep learning-based LBVS called EquiVS to learn molecule representations from conformers for bioactivity prediction. Specifically, graph convolutional network (GCN) and equivariant graph neural network (EGNN) are sequentially stacked to learn high-order molecule-level and conformer-level representations, followed by attention-based deep multiple-instance learning (MIL) to aggregate these representations and then predict the potential bioactivity for the query molecule on a given target. We conducted various experiments to validate the data quality of our benchmark dataset, and confirmed EquiVS achieved better performance compared with 10 traditional machine learning or deep learning-based LBVS methods. Further ablation studies demonstrate the significant contribution of molecular conformation for bioactivity prediction, as well as the reasonability and non-redundancy of deep learning architecture in EquiVS. Finally, a model interpretation case study on CDK2 shows the potential of EquiVS in optimal conformer discovery. The overall study shows that our proposed benchmark dataset and EquiVS method have promising prospects in virtual screening applications.

The graph model enables a broad range of analysis, thus graph processing is an invaluable tool in data analytics. At the heart of every graph processing system lies a concurrent graph data structure that stores the graph. Such a data structure needs to be highly efficient for both graph algorithms and queries. Due to the continuous evolution, the sparsity, and the scale-free nature of real-world graphs, graph processing systems face the challenge of providing an appropriate graph data structure that enables both fast analytical workloads and low-memory fast graph mutations. Existing graph structures offer a hard tradeoff between read-only performance, update friendliness, and memory consumption upon updates. In this paper, we introduce CSR++, a new graph data structure that removes these tradeoffs and enables both fast read-only analytics and quick and memory-friendly mutations. CSR++ combines ideas from CSR, the fastest read-only data structure, and adjacency lists to achieve the best of both worlds. We compare CSR++ to CSR, adjacency lists from the Boost Graph Library, as well as state-of-the-art update-friendly graph structures: LLAMA, STINGER, GraphOne, and Teseo. In our evaluation, which is based on popular graph processing algorithms executed over real-world graphs, we show that CSR++ remains close to CSR in read-only concurrent performance (within 10% on average), while significantly outperforming CSR (by an order of magnitude) and LLAMA (by almost 2×) with frequent updates. We also show that both CSR++’s update throughput and analytics performance exceed that of several state-of-the-art graph structures, while maintaining low memory consumption when the workload includes updates.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

Existing Knowledge Graph (KG) models for commonsense question answering present two challenges: (i) existing methods retrieved entities related to questions from the knowledge graph, which may extract noise and irrelevant nodes, and (ii) lack of interaction representation between questions and graph entities. However, current methods mainly focus on retrieving relevant entities with some noisy and irrelevant nodes. In this paper, we propose a novel Retrieval-augmented Knowledge Graph (RAKG) model, which solves the above issues through two key innovations. First, we leverage the density matrix to make the model reason along the corrected knowledge path and extract an enhanced knowledge graph subgraph. Second, we fuse representations of questions and graph entities through a bidirectional attention strategy, in which two representations fuse and update by Graph Convolutional Network (GCN). To evaluate the performance of our method, we conduct experiments on two widely-used benchmark datasets CommonsenseQA and OpenBookQA. The case study gives insight into findings that the augmented subgraph provides reasoning along the corrected knowledge path for question answering.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

In considering knowledge graphs in a diverse range of domains of interest, graph neural networks have demonstrated significant improvements in node classification and prediction when applied to graph representation with learning node embedding to effectively represent hierarchical properties of graphs. DiffPool is a deep-learning approach using a differentiable graph pooling technique that generates hierarchical representations of graphs. In operation DiffPool is a differentiable graph pooling technique that generates hierarchical representations of graphs. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep graph neural network with nodes mapped sets of clusters. However, control of the learning process is difficult given the complexity and large number of parameters on an `end-to-end’ model. To address this difficulty we propose an novel approach termed FPool which is predicated on the basic approach adopted in DiffPool (where pooling is applied directly to node representations). Methods designed to enhance data classification have been developed and evaluated using a number popular and publicly available sensor data sets. Experimental results for FPool demonstrate improved classification and prediction performance when compared to alternative methods. Moreover, FPool shows an important reduction in the training time over the basic DiffPool framework.

Metabolic pathways provide key information to achieve a better understanding of life and all its processes; this is useful information for the improvement of medicine, agronomy, pharmacy, and other similar areas. The main analysis tool used to study these pathways is based on the idea of pathway comparison, using graph data structures. Metabolic pathway comparison has been defined as a computationally complex task \cite{ay2011submap,abaka2013campways}. In previous work from 2017, two different approaches that simplify the problem of comparing pathways represented as graphs were introduced. The first algorithm consists of the transformation of a two-dimensional graph structure, representing a metabolic pathway, to a one-dimensional structure and thus aligning the corresponding data using a reduced 1 dimension string. The second algorithm consists of performing a paired analysis between reactions in pathways and thus eliminating all similarities, finally, showing these differences to the user. The suggestion is to use the information provided by these algorithms as a previous analysis to a deeper, more expensive, comparison tool use. Here we provide an extension of this work with more data and deeper analysis. These methods have shown to be an effective way to treat the problem of metabolic pathway comparison as listed in the discussion and results section. Our results show evidence of a quick, simple and effective way to resolve the described problem.

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We address the following question how large should be a graph describing connections between discrete thermodynamic states to guarantee the appearance of thermodynamic cycles? The Ramsey theory supplies the answer to this question. Direct graphs emerging from the chains of irreversible thermodynamic processes are considered. In any complete directed graph, representing the thermodynamic states of the system the Hamiltonian path is found. Transitive thermodynamic tournaments are addressed. The entire transitive thermodynamic tournament built of irreversible processes does not contain a cycle of length 3, or in other words, the transitive thermodynamic tournament is acyclic and contains no directed thermodynamic cycles.

The realization of the third-generation artificial intelligence (AI) requires the evolution from perceptual intelligence to cognitive intelligence, where knowledge graphs may not meet the practical needs anymore. Based on the dual channel theory, cognitive graphs are established and developed through coordinating the implicit extraction module and the explicit reasoning module as well as integrating knowledge graphs, cognitive reasoning and logical expressions, which have achieved successes in multi-hop question answering. It is desired for cognitive graphs to be widely used in advanced AI applications such as large-scale knowledge representations and intelligent responses, promoting the development of Al dramatically. This review discusses cognitive graphs systematically and elaborately, including basic concepts, generations, theories and technologies. Moreover, we try to predict the development of cognitive intelligence in the short-term future and further enlighten more researches and studies.

Abnormal connections in brain networks of healthy people always bring the problems of cognitive impairments and degeneration of specific brain circuits, which may finally result in Alzheimer’s disease (AD). Exploring the development of the brain from normal controls (NC) to AD is an essential part of human research. Although connections changes have been found in the development, the connection mechanism that drives these changes remain incompletely understood. The purpose of this study is to explore the connection changes in brain networks in the process from NC to AD, and uncover the underlying connection mechanism that shapes the topologies of AD brain networks. In particular, we propose a model named MINM from the perspective of topology-based mutual information to achieve our aim. MINM concerns the question of estimating the connection probability between two cortical regions with the consideration of both the mutual information of their observed network topologies and their Euclidean distance in anatomical space. In addition, MINM considers establishing and deleting connections, simultaneously, during the networks modeling from the stage of NC to AD. Experiment results show that MINM is sufficient to capture an impressive range of topological properties of real brain networks such as characteristic path length, network efficiency, and transitivity, and it also provides an excellent fit to the real brain networks in degree distribution compared to experiential models. Thus, we anticipate that MINM may explain the connection mechanism for the formation of the brain network organization in AD patients.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik>0; αik=0; αik is not defined; αik<0. Following coloring procedure is introduced: we connect the pairs of points for which αik>0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik<0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik>0 or αik<0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

It has recently been shown that, contrary to the wide belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This paper extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via a counterexample, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing.

Traffic congestion and frequent traffic accidents have become main problems affecting urban traffic. Effective location prediction of vehicle trajectory can help alleviate traffic congestion, reduce the occurrence of traffic accidents, and optimize the urban traffic system. Vehicle trajectory is closely related to the surrounding Points of Interest (POI). POI can be considered as the spatial feature and can be fused with trajectory points to improve prediction accuracy. A Local Dynamic Graph Spatiotemporal- Long Short-Term Memory (LDGST-LSTM) is proposed in this paper to extract and fuse the POI knowledge and realize next location prediction. POI semantic information is learned by constructing the traffic knowledge graph, and spatial and temporal features are extracted by combining Graph Attention Network (GAT) and temporal attention mechanism. Moreover, the weights of POI that influence location prediction are visualized to improve the interpretability of the proposed model. The effectiveness of LDGST-LSTM is verified on two datasets, including Chengdu taxi trajectory data in October 2018 and August 2014. The accuracy and robustness of the proposed model are significantly improved compared with the benchmark models.

In bioinformatics research, traditional machine learning methods have demonstrated efficacy in addressing Euclidean data. However, real-world data often encompasses non-Euclidean forms, such as graph data, which contain intricate structural patterns or high-order relationships that elude conventional machine-learning approaches. Representation learning seeks to derive valuable data representations from enhancing predictive or analytic tasks, capturing vital patterns and structures. This method has proven particularly beneficial in bioinformatics and biomedicine, as it effectively handles high-dimensional, sparse data, detects complex biological patterns, and optimizes predictive performance. In recent years, graph representation learning has become a popular research direction. It embeds graphs into a low-dimensional space while preserving the structural and attribute information of the graph, enabling better feature extraction for downstream tasks. This study extensively reviews representation learning advancements, particularly in the research of representation methods since the emergence of COVID-19. We begin with an analysis and classification of neural network-based language model representation learning techniques as well as graph representation learning methods. Subsequently, we explore their methodological innovations in the context of COVID-19, with a focus on the domains of drugs, public health, and healthcare. Furthermore, we discuss the challenges and opportunities associated with graph representation learning. This comprehensive review presents invaluable insights for researchers as it documents the development of COVID-19 and offers experiential lessons to preempt future infectious diseases. Moreover, this study guides future bioinformatics and biomedicine research methodologies.

Generally, when cognitive radio users are in Underlay mode, through the analysis of the electromagnetic spectrum in time, frequency, space, and field of multiple dimensional data accounts for judging the inherent correlation of the radio spectrum used/idle state, this is the realization of cognitive radio users (secondary users, SUs) efficient access to the foundation of the limited spectrum resources. Therefore, how to efficiently use of spectrum status of each SU implementation of reception multidimensional combination forecasting is the core of this paper addressing the problem. In this paper, we propose a deep-learning hybrid model called TensorGCN-LSTM based on the tensor data structure. The model treats SUs deployed at different spatial locations under the same frequency and the spectrum status of SUs themselves under different frequencies in the task area as nodes and constructs two types of graph structures. Graph convolutional operations are used to sequentially extract corresponding spatial-domain and frequency-domain features from the two types of graph structures. Then, the long short-term memory (LSTM) model is used to fuse the spatial, frequency, and temporal features of the cognitive radio environment data. Finally, the prediction task of the spectrum distribution situation is accomplished through fully connected layers. Specifically, the model constructs a tensor graph based on the spatial similarity of SUs' locations and the frequency correlation between different frequency signals received by SUs, which describes the electromagnetic wave's dependency relationship in spatial and frequency domains. LSTM is used to capture the electromagnetic wave's dependency relationship in the temporal domain. To evaluate the effectiveness of the model, we conducted ablation experiments on LSTM, GCN, GC-LSTM, and TensorGCN-LSTM models using simulated data. The experimental results show that our model achieved better prediction performance in RMSE, and the correlation coefficient R2 of 0.8753 also confirmed the feasibility of the model.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

Constructing new graph from the graph's parameters and related notions in the way that, the study on the new graph and old graph in their parameters could be facilitated. As graph, new graph has some characteristics and results which are related to the structure of this graph. For this purpose, regular graph is considered so the internal relation and external relation on this new graph are studied. The kind of having same number of edges when this number is originated by common number of graphs like maximum degree, minimum degree, domination number, coloring number and clique number, is founded in the word of having regular graph

We studied generalization of a method for extending configurational studies to variables that are not exclusively geographical, in order to allow investigation of generic relationships in the built environment. We observed a number of limitations of the classical approach of configurational studies and we considered how a complex analytical method could be implemented in the study of non-topological variables, such as land use, noise pollution and financial or property rents. In order to do this we established a system of relationships based on a labeled primary graph. Categorization of the labels of the links was performed on a generic variable, specifically, the predominant use of roads. The graph was then contracted using an optimization algorithm, which we describe. The algorithm allows the network to be reduced to a more streamlined system that can better analyze the relationships between the different categories. Application of the method showed that it is faster to identify weaknesses in urban networks, and then take measures to resolve them. The case study concerns the pedestrianization of the Colosseum area in Rome.

This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM’s advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.

The COVID-19 pandemic has resulted in a wide range of spatial interventions to slow down the spread of the virus. The spatial limitations of narrow public circulation spaces within informal settlements, which house over one billion people around the world, make it impossible for pedestrians to practice physical distancing (or social distancing). In this paper, we propose a flexible mathematical method, named the Cluster Lane Method, for turning a planar circulation network of any size or complexity into a network of unidirectional lanes, making physical distancing possible in narrow circulation spaces by limiting face-to-face interactions. New notions and theorems about oriented graphs in graph theory are introduced. The paper ends with a discussion of the potential implementation of this cost-efficient, low-tech, sustainable solution, and with the introduction of a novel unidirectional tactile paving for the visually impaired.

In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily

Ensuring the integrity of scientific literature is essential for advancing knowledge and research. However, the credibility and trustworthiness of scholarly publications are compromised by manipulated citations. Traditional methods, such as manual inspection and basic statistical analyses, have limitations in detecting intricate patterns and subtle manipulations of citations. In recent years, network-based approaches have emerged as promising techniques for identifying and understanding citation manipulation. This study introduces a novel method to identify potential citation manipulation in academic papers using perturbations of a deep embedding model. The key idea is to reconstruct meaningful connections represented by citations within a network by exploring slightly longer alternative paths. These indirect pathways enable the recovery of original and reliable citations while estimating their trustworthiness. The investigation takes a comprehensive approach to link prediction, leveraging the consistent behavior of prominent connections when exposed to network perturbations. Through numerical experiments, the method demonstrates a high capability to identify reliable citations as the core of the analyzed data and to raise suspicions about unreliable references that may have been manipulated.

In the last decade several projects have been developed for the digitization and semantization of cultural heritage data. They were developed to preserve and maintain this heritage, but bringing it closer to all types of users and allowing access to this information to other sectors such as tourism, education, etc. In these developments, web technologies are combined, along with the use of knowledge graphs and interactive visualisation tools. Although remarkably interesting projects have been developed, in those projects, the data visualization tools are usually focused on the project context. This makes it difficult to reuse these jobs. Additionally, there are peculiarities of cultural heritage data considered with little depth, such as uncertainty, spatial and temporal granularity, as well as other aspects, such as relationships between data. In this article, these problems are described and based on other works such as VUMO or VISO, the design of an ontology that formalizes how to visualise this information is proposed, considering these problems. In addition, the development of a platform that allows the visualisation of this information through a web application and its evaluation of its use in projects such as SILKNOW, or Arxiu Valencià del Disseny is exposed

Formation in soccer is among the most important tactical choices for a successful match.Herein, the simulations of 420000 match-plays have been performed varying the formation, the number of opponents that are actively pressing the team, the speed of the opponents in attempting a pass interception. Dribbling has been neglected. The match-play ends either with a successful series of passes from a central back to the line of the strikers or with the opponents that steal the ball. In this work, I demonstrate that 3-4-3 formation, which is among the most employed formations, relates to the highest probability of success.

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.

Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China¹. There are more than one hundred cases outside of China, affecting a dozen of countries globally². The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed³. Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days ^4,5. However, major factors such as transportation and cultural customs have not been weighed enough. Our model is not set out for precise prediction of the number of infected cases, rather, it is meant for a glance of the dynamics under a public epidemic emergency situation and of different contributing factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

Plants produce a diverse portfolio of sesquiterpenes that are important in their response to herbivores and the interaction with other plants. Their biosynthesis from farnesyl diphosphate depends on the sesquiterpene synthases. Here, we investigate to what extent metabolic pathways can be reconstructed just from knowledge of the final product and the reaction mechanisms catalyzed by sesquiterpene synthases. We use the software package MedØlDatschgerl (MØD) to generate chemical networks and elucidate pathways contained in them. As examples, we successfully consider the reachability of the important plant sesquiterpenes β-caryophyllene, α-humulene, and β-farnesene. We also introduce a graph database to integrate simulation results with experimental biological evidence for selected predicted sesquiterpenes biosynthesis.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

This paper presents a new method : HIVEC to learn latent vector representations of graphs in a manner that captures the semantic dependencies of sub-structures. The representations can then be used in machine learning algorithms for tasks such as graph classification, clustering etcetera. The method proposed is unsupervised and uses the information of co-occurrence of sub-structures. It introduces a notion of hierarchical embeddings that allows us to avoid repetitive learning of sub-structures for every new graph. As an alternative to deep learning methods, the edit distance similarity between sub-structures is also used to learn vector representations. We compare the performance of these methods against previous work.

We introduce the Concept-Model-Graph-View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision-making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.

This paper presents the Advanced Syntactic-Graph Convolutional Model (ASGCM), a pioneering approach in Aspect-Based Sentiment Analysis (ABSA) that integrates syntactic dependency features within a graph convolution framework. ASGCM stands out for its novel use of dependency edge encoding and tag-based graph convolutions, providing a fine-grained analysis of sentiments associated with specific aspects in text. This model meticulously captures the intricacies of syntactic structures, thereby offering enhanced precision in sentiment analysis. Notably, ASGCM incorporates a dual-layer graph convolution system: one layer processes syntactic dependencies (edges), while the other interprets semantic roles (tags), ensuring a comprehensive understanding of both structural and contextual elements in text. We rigorously tested ASGCM on multiple datasets, including both English and Chinese languages, and our findings reveal a significant improvement in sentiment classification accuracy compared to existing models. The versatility of ASGCM makes it a robust tool for diverse linguistic environments, setting a new standard for ABSA methodologies.

Consensus algorithms are the core technology of blockchain and a focus in the current distributed system research. The consensus algorithms are widely used in distributed systems, it has solved the decentralization problem. The traditional consensus algorithm needs the process of node legitimacy checking, identity authentication, and primary node view change, so the time cost of reaching an agreement between nodes is still exponential. In response to the problem, a lightweight consensus algorithm based on graph (LCAG) is proposed for the Internet of Things (IoT) in this paper, which is proposes an access control table, and reaches an agreement among nodes by calculating the probability of nodes in the control table, and reduces the time overhead of the reaching an agreement in distributed systems. We have carried out simulation experiments for the new algorithm, and the experiments show that: the new algorithm needs less time overhead than the classical Byzantine algorithm need, as well as Byzantine Generals problem (BGP), practical Byzantine fault-tolerant algorithm (PBFT) and directed acyclic graph (DAG) algorithm, and so on. The new algorithm can be applied to the devices of IoT, which have limited computing power.

It is difficult to effectively operate a dual-arm robot using only the information written in a cooking recipe. To cope with this problem, this paper proposes a graph based approach on bimanual cooking motion planning from a cooking recipe. In our approach, we first decompose the cooking recipe into graph elements. Then, we try to connect the graph elements taking into account the attributes of the input/output nodes. If two graph elements cannot be connected each other, we search for a graph element that can be inserted between them from the database of graph elements. Since the constructed graph includes the whole sequence of the robot’s motions to perform the cooking task, we can generate a task sequence of a dual-arm manipulator simultaneously performing two different tasks by using two arms. Through experimental study, we show that it is possible to generate robot motions from a cooking recipe and perform the cooking motions while simultaneously moving the left and right arms.

With the development of data science, more and more machine learning technologies have been designed to solve complicated and challenging real-world tasks containing a large volume of data. And many significant real-world datasets contain data in the form of networks or graphs. Graph Neural Networks is one of the powerful machine learning tools, which could provide a perfect solution to processing a large amount of non-Euclidean data. And because most bio information data in bioinformatics is in the non-Euclidean domain, Graph Neural Networks could then directly be applied to solve problems in bioinformatics. Much research has been done in the field of GNN, and there are also some surveys related to GNN and its applications. However, there has been little research focusing on GNN in bioinformatics, and we think in the future we could better utilize GNN in the field of biology, so we would like to write a literature review to help take a comprehensive look at GNN and their applications in the field of bioinformatics. In this paper, we would first introduce SOTA models in Graph Neural Networks, and second, introduce their applications in bio information. And then we would provide future directions of Graph Neural Networks in bioinformatics.

Forest fire identification is important for forest resource protection. Effective monitoring of forest fires requires the deployment of multiple monitors with different viewpoints, while most traditional recognition models can only recognize images from a single source. By ignoring the information from images with different viewpoints, these models produce high rates of missed and false alarms. In this paper, we propose a graph neural network model based on the similarity of dynamic features of multi-view images to improve the accuracy of forest fire recognition. The input features of the nodes on the graph are converted into relational features of different gallery pairs by establishing pairs (nodes) representing different viewpoint images and gallery images. The new feature library relationship is used to update the image gallery with dynamic features in order to achieve the estimation of similarity between images and improve the image recognition rate of the model. In addition, to reduce the complexity of image pre-processing process and extract key features in images effectively, this paper also proposes a dynamic feature extraction method for fire regions based on image segment ability. By setting the threshold value of HSV color space, the fire region is segmented from the image, and the dynamic features of successive frames of the fire region are extracted. The experimental results show that, compared with the baseline method Resnet, this paper's method is more effective in identifying forest fires, and its recognition accuracy is improved by 2%. And the scheme of this paper can adapt to different forest fire scenes, with better generalization ability and anti-interference ability.

Recent years have seen the growing adoption of non-relational data models for representing diverse, incomplete data. Among these, the RDF graph-based data model has seen ever-broadening adoption, particularly on the Web. This adoption has prompted the standardization of the SPARQL query language for RDF, as well as the development of a variety of local and distributed engines for processing queries over RDF graphs. These engines implement a diverse range of specialized techniques for storage, indexing, and query processing. A number of benchmarks, based on both synthetic and real-world data, have also emerged to allow for contrasting the performance of different query engines, often at large scale. This survey paper draws together these developments, providing a comprehensive review of the techniques, engines and benchmarks for querying RDF knowledge graphs.

The prediction of drug--target interactions is always a key task in the field of drug redirection. However, traditional methods of predicting drug--target interactions are either mediocre or rely heavily on data stacking. In this work, we merged heterogeneous graph information and obtained effective node information and substructure information based on mutual information in graph embeddings. We then learned high quality representations for downstream tasks, and proposed an end--to--end auto--encoder model to complete the task of link prediction. Experimental results show that our method outperforms several state--of--art models. The model can achieve the area under the receiver operating characteristics (AUROC) curve of 0.959 and area under the precise recall curve (AUPR) of 0.848. We found that the mutual information between the substructure and graph--level representations contributes most to the mutual information index in a relatively sparse network. And the mutual information between the node--level and graph--level representations contributes most in a relatively dense network.

Identifying fake news on the media has been an important issue. This is especially true considering the wide spread of rumors on the popular social networks such as Twitter. Various kinds of techniques have been proposed for automatic rumor detection. In this work, we study the application of graph neural networks for rumor classification at a lower level, instead of applying existing neural network architectures to detect rumors. The responses to true rumors and false rumors display distinct characteristics. This suggests that it is essential to capture such interactions in an effective manner for a deep learning network to achieve better rumor detection performance. To this end we present a simplified aggregation graph neural network architecture. Experiments on publicly available Twitter datasets demonstrate that the proposed network has performance on a par with or even better than that of state-of-the-art graph convolutional networks, while significantly reducing the computational complexity.

Graph entropies have been used to interpret the complexity of the networks. There are various graph entropies in the literature. In this note a new graph entropy is defined which is based on the dominating sets of the graphs. Moreover the entropy of some classes of the graphs is obtained

In mathematics, one always aims to obtain new frameworks from specific ones. This also stratified to the regality of graphs, where one can produce numerous new graphs from a specific set of graphs. In this work we define some classes of pyramid graphs created by a gear graph and we derive straightforward formulas of the complexity of these graphs, using linear algebra matrix analysis techniques and employing knowledges of Chebyshev polynomials.

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q].

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

The independent set, IS, on a graph $G=(V,E)$ is $V^{*}\subseteq V$ such that no two vertices in $V^{*}$ have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. $V^{*}\subseteq V$ is a vertex cover, i.e. VC of $G=(V,E)$ if every $e\in E$ is incident upon at least one vertex in $V^{*}$ . $V^{*}\subseteq V$ is dominating set, DS, of $G=(V,E)$ if $\forall v\in V$ either $v\in V^{*}$ or $\exists u\in V^{*}$ and $(u,v)\in E$ . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if $k=\Theta (log\mid V\mid )$ then MIS, MVC and MDS can be computed in polynomial time and if $k=O\left({(log\mid V\mid )}^{\alpha }\right)$ , where $\alpha <1$ , then MCV and MCD can be computed in polynomial time. If $k=\Theta \left({(log\mid V\mid )}^{1+ϵ}\right)$ , for $ϵ>0$ , then MIS, MVC and MDS require quasi-polynomial time. If $k=\Theta (log\mid V\mid )$ then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.

We address the problem of finding a unique graph embedding that best describes a graph's "topology". This issue is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default "topology" of periodic graphs.

Due to the inclusion of both the principles and divination methods, the study of Yijing (Yijing) becomes more complex. The complex data types, diverse semantic relationships, and unclear influencing mechanisms in Yijing pose challenges to its scientific research. Knowledge graph, as an advanced way of organizing knowledge, can provide technical support in exploring the hidden connections and knowledge structure within text resources. This paper proposes a method of constructing a Yijing knowledge graph based on Neo4j. By analyzing the concepts, entities, and various related relationships in Yijing, the method discusses the basic architecture, data model, and implementation steps of constructing the Yijing knowledge graph. It also extracts, integrates, and structures the Yijing knowledge, allowing for inquiries, associations, and reasoning about the knowledge and its various elements. By adopting a top-down approach, the paper reconstructs the fundamental knowledge system of the Yijing, including yin-yang, the five elements, generation and restriction, 64 hexagrams, and six lines(yao). It establishes a knowledge graph pattern layer and a data layer that encompass concepts, attributes, and relationships. With the technical support of the Neo4j platform, the visualization and retrieval of Yijing knowledge are realized, providing new ideas and methods for studying the mechanisms of the Yijing. The proposed method of constructing a Yijing knowledge graph can be expanded to other types of ancient scripture knowledge graph research and can be applied to the field of digital humanities, promoting in-depth cross-disciplinary research and integration.

Knowledge graphs (KGs) play a crucial role in many applications, such as question answering, but incompleteness is an urgent issue for their broad application. Much research in knowledge graph completion (KGC) has been performed to resolve this issue. The methods of KGC can be classified into two major categories: rule-based reasoning and embedding-based reasoning. The former has high accuracy and good interpretability, but a major challenge is to obtain effective rules on large-scale KGs. The latter has good efficiency and scalability, but it relies heavily on data richness and cannot fully use domain knowledge in the form of logical rules. We propose a novel method that injects rules and learns representations iteratively to take full advantage of rules and embeddings. Specifically, we model the conclusions of rule groundings as 0-1 variables and use a rule confidence regularizer to remove the uncertainty of the conclusions. The proposed approach has the following advantages: 1) It combines the benefits of both rules and knowledge graph embeddings (KGEs) and achieves a good balance between efficiency and scalability. 2) It uses an iterative method to continuously improve KGEs and remove incorrect rule conclusions. Evaluations on two public datasets show that our method outperforms the current state-of-the-art methods, improving performance by 2.7% and 4.3% in mean reciprocal rank (MRR).

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

As various services have been generating large scale graphs to represent multiple relationships between objects, studies have been conducted to obtain subgraphs with particular patterns. In this paper, we propose a distributed query processing method to efficiently search a subgraph for a large graph on Spark. To reduce unnecessary processing costs, the search order is determined by filtering scores using the probability distribution. The partitioned queries are searched in parallel in the distributed graph of each slave node according to the search order, and the local search results obtained from each slave node are combined and returned. The query is partitioned in triplets based on the determined search order. The performance of the proposed method is compared with the performance of existing methods to demonstrate its superiority.

The popularity and development of social media has made it more and more convenient to spread rumors, and it has become especially important to detect rumor information from massive amounts of information. Most of the traditional rumor detection methods use content characteristics or propagation structure to mine rumor characteristics, ignoring the fusion characteristics of content and structure and their interaction characteristics. Therefore, a novel rumor detection method based on heterogeneous convolutional networks is proposed. Firstly, this paper constructs a heterogeneous map of joint rumor content and propagation structure to explore the interaction between content and propagation structure during rumor propagation and obtain rumor representation. On that basis, this paper uses the deep residual graph convolutional neural network to construct the content and structure interaction information of the current network propagation model. Finally, this paper uses the two datasets of Twitter15 and Twitter16 to verify the proposed method. Experimental results show that the proposed method has higher detection accuracy than the traditional rumor detection method.

This report gives a comprehensive summary of two problems about graph convolutional networks (GCNs): over-smoothing and heterophily challenges, and outlines future directions to explore.

The chemical feedback between building blocks in templated polymerization of diblock copolymers and their consecutive micellization was studied for the first time by means of coarse-grained molecular dynamics simulations. Using a stochastic polymerization model, we were able to reproduce the experimental findings on the effect of chemical feedback on the polymerization rates at low and high solution concentrations. The size and shape of micelles were computed using a newly development software in python conjugated with graph theory. In full agreement with the experiments, our simulations revealed that micelles formed by the templated micellization are more spherical and have lower radius of gyration than those formed by the traditional two-step micellization method. Understanding the underlying mechanisms in templated reaction/assembly of polymers will help for rational design of new synthetic supramolecular materials.

We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are yikx=αikx+βik i,k=1...6, αik≠0. We color the edges connecting the points for which αik&gt;0 holds with red, and the edges for which αik&lt;0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R3,3=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.

We present a Deep Learning generative model specialized to work with graphs with a regular geometry. It is build on a Variational Autoencoder framework and employs Graph convolutional layers in both encoding and decoding phases. We also introduce a pooling technique (ReNN-Pool), used in the encoder, that allows to downsample graph nodes in a spatially uniform and highly interpretable way. In the decoder, a symmetrical un-pooling technique is used to retrieve the original dimensionality of graphs. Performance of the model are tested on the standard Sprite benchmark dataset, a set of 2D images of video game characters, adequately transforming images data into graphs, and on the more realistic use-case of a dataset of cylindrical-shaped graph data that describe the distributions of the energy deposited by a particle beam in a medium.

In the modern world where research is taking a huge leap, the collaboration network between authors is also expanding, increasing the probability of different authors coming together to work on the same project, same research paper making them co-authors. In coauthorship, link prediction is used to anticipate new interactions between its members that are likely to occur in the future. Researchers have concentrated their efforts on studying and suggesting methods for providing effective reviews for authors who can collaborate on a scientific endeavor. In order to provide a precise link prediction, a graph database approach is proposed in this paper using nodes to determine most possible co-authors in future. In order to forecast the connections, we preprocessed the data set for the maximum relative contents. A supervised learning approach is used to execute the solution, which includes random forest classifier and logistic regression. The first findings of our technique reveal that the total of two author node’s research collaboration indices has the greatest influence on the performance of supervised link prediction than that of the traditional approach, which stimulates us to conduct further study on employing such a forecast.

The study of the brain networks using analysis of electroencephalography (EEG) data based on statistical dependencies (functional connectivity) and mathematical graph theory concepts is common in neuroscience and cognitive sciences for examinations of patient and healthy individuals. The Consciousness Fields according to Taheri theory and applications in the optimization of system under study have been investigated in various studies. In this study, we examine the results of working with Faradarmani Consciousness Field (FCF) in the brain of Faradarmangars. Faradarmangars are one of the necessary components in mind mediation of the function of Faradarmani Consciousness Fields according to Taheri. For this purpose, the functional and effective connectivity and the corresponding brain graphs of EEG from the brain of Faradarmangars is compared with that of non Faradarmangar groups during FCF connection. According to the results of the present study, the brain of the Faradarmangars shows significant decreased activity in delta (BA8), beta2 (BA4/6/8/9/10/11/32/44/47) and beta3 (in 34 of 52 BA) frequency bands mainly in frontal lobe and after that in parietal and temporal lobes in the comparison with the non Faradarmangars. Moreover, the functional and effective connectivity analysis in the frontal network shows dominant multiple decreased connectivity mainly in the case of beta3 frequency band in all parts of the frontal network. On the other hand, the graph theory analysis of the Faradarmangar brain shows an increase in the activity of the O2-T5-F4-F3-FP2-F8 areas and significant decrease in the characteristic path length and increases in global efficiency, clustering coefficient and transitivity. In conclusion, the unique higher graph function efficiency and the reduction in the brain activity and connectivity during the Faradarmani Consciousness Field mind mediation, shown the passive and detector like function of the human brain in this task.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

Surrogate model based optimization method is widely-used to accelerate the design and optimization process~\cite{marler2004survey}. The input of regression model used in the surrogate model are numbers, which requires users to parametrize the geometries. In this paper, a new parameterization-free surrogate model is introduced and its corresponding uncertainty quantification and sensitivity analysis method are discussed. The input of new surrogate model methods is surface mesh of simulation domain. \Gls{gnns} is used to extract geometric information, and \Gls{cnns} is used to predict contours. This framework bypasses parameterization,as a consequence, uncertainties introduced by manual parameterization is reduced. However, such changes compared with conventional surrogate model methods impose great challenge on uncertainties quantification and sensitivity analysis. Uncertainties quantification in this paper means the error bar of prediction results, which is calculated by Gaussian Process Regression method in current surrogate method. In this paper, a new quantification method achieved by Kullback-Leibler divergence (KLD) is introduced. And the sensitivity analysis is conducted by Automatic Differentiation, which gives a Jacobian matrix of inputs. The method and analysis mentioned above are demonstrated by a low-pressure steam turbine rotator and its exhaust system.

Existing proofs of the 4-color theorem succeeded by establishing an unavoidable set of reducible configurations. By this device, their authors showed that a minimum counterexample cannot exist. G.D. Birkhoff proved that a minimum counterexample must satisfy a connectivity property that is referred to in modern parlance as internal 6-connectivity. We show that a minimum counterexample must also satisfy a coloring property, one that we call Kempe-locking. We define the terms Kempe-locking configuration and fundamental Kempe-locking configuration. We provide a heuristic argument that a fundamental Kempe-locking configuration must be of low order and then perform a systematic search through isomorphism classes for such configurations. We describe a methodology for analyzing whether an arbitrary planar triangulation is Kempe-locked; it involves deconstructing the triangulation into a stack of configurations with common endpoints and then creating a bipartite graph of coloring possibilities for each configuration in the stack to assess whether certain 2-color paths can be transmitted from the configuration's top boundary to its bottom boundary. All Kempe-locked triangulations we discovered have two features in common: (1) they are Kempe-locked with respect to only a single edge, say $xy$, and (2) they have a Birkhoff diamond with endpoints $x$ and $y$ as a proper subgraph. On the strength of our various investigations, we are led to a plausible conjecture that the Birkhoff diamond is the only fundamental Kempe-locking configuration. If true, this would establish that the connectivity and coloring properties of a minimum counterexample to the 4-color theorem are incompatible. It would also point to the singular importance of a particularly elegant 4-connected triangulation of order 9 that consists of a triangle enclosing a pentagon enclosing a single vertex.

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph N_n, for n ≥ 2 has been determined. It is further shown that N₃ is chromatically unique.

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

: Biological networks such as protein interaction networks, gene regulation networks and metabolic pathways are examples of complex networks which are large graphs with small-world and scale-free properties. Analysis of these networks has a profound effect on our understanding the origins of life, health and disease states of organisms, and diagnose diseases to aid the search for remedial processes. In this review, we describe main analysis methods of biological networks using graph theory by first defining main parameters such as clustering coefficient, modularity and centrality. We then survey fundamental graph clustering methods and algorithms followed by the network motif search algorithms with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function carried out by that small network and discovering such a function provides an insight to the overall function of the organism. Lastly, we review network alignment algorithms that achieve to find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor and finding such relationship may help researchers derive ancestral relationships and predict the future evolution of organisms to enable designing new drugs. We conclude by the current challenging areas of biological network analysis using graph theory and parallel processing for high performance analysis

Breast cancer is one of the most common types of malignant tumors worldwide and the leading cause of cancer-related deaths in women. According to the latest report from the World Health Organization, breast cancer has surpassed lung cancer, becoming the most diagnosed cancer globally. Herein, a systematic, quantitative, and visual analysis of the scientific achievements in natural products research and development for breast cancer over the past 30 years is presented. The study utilizes bibliometric and knowledge graph visualization techniques to analyze the trends, co-occurrence of keywords, cooperative networks, cited literature, and research hotspots in the field. The analysis shows that breast cancer natural drug development involves mutual cooperation between multiple countries, with China, the United States, and India being the most active players. Pharmacology is the discipline with the largest number of articles published in nearly 30 years. The study also reveals that the extraction of drugs from organisms and their metabolites is an important direction in the current development of anticancer drugs. The development of natural medicines for breast cancer together with the mining of genetic knowledge play an important role in treating human breast cancer. The research presented here provides insights into the current state of natural product research and development for breast cancer, and highlights the need for strengthening mutual communication and cooperation between countries and scientific research institutions to enhance the development of breast cancer treatment technologies and natural medicines.

In recent years, intensive work has been carried out to achieve maximum energy production in photovoltaic power plants. Today, this challenge has to be solved for arrays of solar panels that move with the object on which they are installed (vehicles, trucks, ships, etc.). The present work tries to find the best solution for both constant voltage systems and for cases of maximum intensity. Once found, these solutions will be applied in real time for the dynamic recharging of battery packs, trying to achieve energetically autonomous vehicles.To solve these situations, a new computational method of voltage and amperage calculation has been developed in this paper, based on Dijkstra’s minimum path finding algorithm on graph theory, adapted to electrical circuits. For this purpose, panel performance analysis sensors, developed at the University of Malaga, have been combined with different electronic solutions (wifi relay devices using esp8266 or similar chips) achieving an accurate and sufficiently fast solution at very low cost. With this, series or parallel configurations can be carried out depending on the type of energy generation sought. The theoretical solutions using Minkowski paths, achieved in the past, have been simulated and subsequently constructed in this article, indicating the diagrams necessary for their realisation.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another denitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

Zero-Knowledge Proofs ZKP provide a reliable option to verify that a claim is true without giving detailed information other than the answer. A classical example is provided by the ZKP based in the Graph Isomorphism problem (GI), where a prover must convince the verifier that he knows an isomorphism between two isomorphic graphs without publishing the bijection. We design a novel ZKP exploiting the NP-hard problem of finding the algebraic ideal of a multivariate polynomial set, and consequently resistant to quantum computer attacks. Since this polynomial set is obtained considering instances of GI, we guarantee that the protocol is at least as secure as the GI based protocol.

In recent years, there has been significant growth in the ubiquity and popularity of three dimensional(3D) point clouds, with an increasing focus on the classification of 3D point clouds. To extract richer features from point clouds, many researchers have turned their attention to various point set regions and channels within irregular point clouds. However, this approach has limited capability in attending to crucial regions of interest in 3D point clouds and may overlook valuable information from neighboring features during feature aggregation. Therefore, this paper proposes a novel 3D point cloud classification method based on global attention and adaptive graph convolution. The method consists of two main branches: the first branch com-putes attention masks for each point, while the second branch employs adaptive graph convolu-tion to extract global features from the point set. It dynamically learns features based on point interactions, generating adaptive kernels to effectively and precisely capture diverse relationships among points from different semantic parts. Experimental results demonstrate that the proposed model achieves 93.8% in overall accuracy and 90.8% in average accuracy on the ModeNet40 dataset.

In the intricate domain of text analysis, syntactic dependency trees play a crucial role in unraveling the web of relations among entities embedded in the text. These trees provide a structural roadmap, guiding us through the complex syntax to pinpoint the interactions and connections between different entities. However, the challenge lies in sifting through this intricate structure to extract relevant information, a task that requires precision and discernment. Traditional approaches often rely on rule-based pruning methods to simplify these dependency structures, focusing on certain parts while discarding others. Yet, this approach has its pitfalls, as it can overlook critical nuances and connections that are vital for a comprehensive understanding of the text. Addressing this gap, our research introduces the Syntactic Dependency-Aware Neural Networks (SDANNs), a groundbreaking model designed to harness the full power of the entire dependency tree. This approach marks a significant departure from the conventional methods. Instead of the rigid rule-based pruning, SDANNs implement a more flexible and dynamic 'soft-pruning' technique. This method allows the model to adaptively focus on the sub-structures within the dependency tree that are most relevant for understanding the relationships between entities. By doing so, it ensures that no vital information is overlooked, and all potential connections are considered. The efficacy of SDANNs is not just theoretical but has been empirically validated through extensive testing and evaluations across a wide range of tasks. These tasks include the extraction of complex relations spanning multiple sentences, as well as detailed analyses at the sentence level. In each of these scenarios, SDANNs have demonstrated a remarkable ability to leverage the full structural complexity of dependency trees. This capability sets them apart from existing models, enabling a more nuanced and comprehensive analysis of textual relations. The results of these evaluations consistently show that SDANNs not only meet but significantly exceed the performance of prior models. This superiority is evident in the way SDANNs handle the multifaceted and often subtle interactions within the text, offering insights that were previously inaccessible with conventional methods. In summary, the Syntactic Dependency-Aware Neural Networks represent a significant advancement in the field of text analysis. By fully embracing the complexity of syntactic dependency trees and employing a sophisticated 'soft-pruning' approach, SDANNs open new avenues for exploring and understanding the intricate relationships that exist within written language. This model stands as a testament to the potential of combining advanced neural network architectures with a deep understanding of linguistic structures, paving the way for more accurate, nuanced, and comprehensive analyses of text.

In large-scale parallel computing and communication systems, an interconnect network structure is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. In a graph, the vertices and edges are likely to fail, so we must think about the fault tolerance of a graph. Connectivity is an important parameter in the study of faulty tolerance for a graph. In this paper, we study a special class of connectivity: $m$-component connectivity, this is a natural generalization of the classical connectivity of graphs defined in terms of the minimum vertex-cut. Let $F$ is a vertex set of $G$ $(i.e, F\subseteq V(G))$, if the following conditions are satisfied, we say $F$ is a $m$-component cut: $(1)$ $G-F$ is disconnected; $(2)$ the number of components in $G-F$ is greater than or equal to $m$. In another word, the $m$-component connectivity $c\kappa_{m}(G)$ is defined as $min\{|F|~|~F\subseteq V(G)$ and $F$ is a $m$-component cut$\}$. Determining $m$-component connectivity is still unsolved in most interconnection networks even for small $m'$s. Leaf-sort graph is a special Cayley graph, it has many special properties that are different from other Cayley graphs. So we need to pay attention to some of it's special properties when we study it. In this paper, we can get the values: $c\kappa_{3}(CF_{n})=3n-6$ $(n$ is odd$)$ and $c\kappa_{3}(CF_{n})=3n-7$ $(n$ is even$)$ for $n\geq3$; $c\kappa_{4}(CF_{n})=\frac{9n-21}{2}$ $(n$ is odd$)$ and $c\kappa_{4}(CF_{n})=\frac{9n-24}{2}$ $(n$ is even$)$ for $n\geq4$; $c\kappa_{5}(CF_{n})=6n-16$ $(n$ is odd$)$ and $c\kappa_{5}(CF_{n})=6n-18$ $(n$ is even$)$ for $n\geq5$.

Network neuroscience delves into comprehending the intricate arrangement and interactions within the neural networks of the brain. By merging insights from both neuroscience and network theory, it investigates the brain's structure and function through the lens of interconnected nodes (symbolizing brain regions) and edges (symbolizing the connections among these regions) forming a dynamic network. Graph metrics play a pivotal role in neuroscience by providing quantifiable insights into the intricate connectivity patterns within the brain's neural networks. Frequently, nodes are extracted from functional or structural atlases, which can lead to diverse shapes and sizes. Nevertheless, our understanding of how these differing node characteristics and definitions impact the computed graph metrics in neuroimaging data remains limited. This study adopts a data-driven methodology to delineate functional nodes, subsequently examining the influence of their sizes on resultant graph metrics. By employing the Neuromark framework, an entirely automated independent component analysis (ICA) is applied to resting state fMRI data. Through this, functional network connectivity (FNC) matrices are computed—capturing Pearson correlations between component-time courses—while employing a proportional threshold to streamline node connections based on these correlations. Subsequently, various global and local graph metrics are computed, offering insights into network characteristics. Global metrics provide an overarching summary of the network structure, while local measures delve into structural intricacies at the individual component level. Node sizes are computed based on voxel counts surpassing a designated threshold. Next, we calculated the Pearson correlation between the obtained node sizes and the graph metrics, which we term 'node-metric coupling' (NMC). Our findings revealed consistent and noteworthy correlations between the values of graph metrics and the dimensions of brain nodes. To delve deeper into the implications of this correlation, we examined the node-metric coupling within a dataset comprising Alzheimer's disease, mild cognitive impairment, and control subjects. The disparities observed in node-metric coupling among these groups underscore the necessity of accounting for this factor during analysis. The two principal outcomes of this study are as follows: Firstly, the substantial interplay between varying node sizes within a given atlas and the resultant graph metrics; and secondly, the potential utility of node-metric coupling as a viable biomarker for brain disorders. These discoveries hold significant ramifications. While comparing studies employing diverse atlases is already a challenge, our work highlights an additional, critical source of variability: accounting for node sizes. Consequently, the association between intra-atlas node size and graph metric should be thoughtfully acknowledged in future neuroimaging investigations.

In cold-climate regions, road salt is used as a de-icer for winter road maintenance. The applied road salt melts ice and snow on roads, being washed off through storm sewer systems into nearby urban streams, harming the freshwater ecosystem. Addressing the gap in the knowledge regarding the use of deep learning approaches for urban stream water quality forecasting, the present work discusses our implementation of a “Graph Neural Network” - “Sample and Aggregate” (GNN-SAGE) model for forecasting chloride concentrations in the Credit River in Ontario, Canada. The proposed GNN-SAGE is compared to other models, including a Deep Neural Network based transformer (DNN-Transformer) and a benchmarking persistence model for 6 hours forecasting horizon. Ac-cording to the results, the GNN-SAGE model surpasses other models in providing accurate predic-tions of chloride concentrations within the assessed prediction window. Also, a SHAP analysis provides insight into the variables that influence the model’s forecasting, showing the impact of the spatiotemporal neighbouring data from the network and the seasonality variables on the model’s result. The GNN-SAGE model shows potential for use in real-time forecasting of water quality in urban streams, aiding in the development of regulatory policies to protect the vulnerable freshwater ecosystems in urban areas.

Directed acyclic graphs (DAGs) are nonparametric causal path diagrams that have substantial utility as principled representations of disease and healthcare pathways, and of the underlying ‘data generating mechanisms’ these pathways involve. As such, DAGs provide a valuable bridge between: the aetiological knowledge, operational insight and professional experience on which clinical training and practice depend; and the more abstract epistemological and analytical considerations required to extract robust statistical insight from health and healthcare data. DAGs are nonetheless vulnerable to imperfect biomedical paradigms, partial clinical knowledge and limited empirical data. DAGs drawn under such circumstances offer limited scope for statistical insight free from cognitive, analytical or inferential bias if: they misrepresent the data generating mechanisms involved; or ignore the important role that omitted variables (whether measured, unmeasured or unacknowledged) might play therein. To address these weaknesses and broaden the appeal and application of DAGs, this chapter provides ten simple steps that educators can use to improve the analytical competence and statistical confidence of the healthcare students, qualified practitioners and experienced researchers they support. These steps use temporal logic to draw DAGs so as to: reduce reliance on uncertain knowledge, incomplete information, flawed assumptions or guesswork; and avoid, mitigate or acknowledge the errors and biases that each of these incur. The chapter comprises an accessible, non-technical overview of the perspective and thoughtfulness required to generate temporally coherent DAGs as objective representations of the probabilistic causal paths involved in context-specific data generating mechanisms. It encourages a focus on those variables operating as potential sources of analytical or inferential bias when estimating the plausible, probabilistic causal relationship between two pre-specified variables; and specifically addresses the challenges posed by: omitted; time-variant; non-asynchronous; and temporally obscure variables. The chapter includes a worked example based on a published clinical study to demonstrate how each of the steps required to generate temporally-informed DAGs can be applied to: critically appraise the analytical decisions made during applied healthcare research; and inform the decisions required when designing, undertaking and analysing primary and secondary, prospective and retrospective research. The appendices include a summary of ten recommendations for improving the reporting and interrogability of DAGs and DAG-informed analyses.

The origins of directed acyclic graphs (DAGs) date back to the emergence of ‘graph theory’ in the early 1700s (Biggs et al. 1986). DAGs are conceptual or literal, diagrammatic representations of causal paths between variables which are constructed – as their name suggests – on the basis of two over-riding principles: first, that all causal paths are ‘directed’ (i.e. for each pair of variables, only one can represent the cause, while the other must be its consequence); and second, that no direct cyclical paths, or indirect cyclical pathways (comprising sequences of consecutive paths) are allowed, such that no consequence can be considered its own direct or indirect cause (hence ‘acyclic’; Law et al., 2012). As such DAGs reflect the knowledge, presumptions, assumptions and/or speculation of the analyst(s) concerned regarding the causal relationships between each of the variables included therein. Current convention dictates that variables are represented as nodes/vertices, and that any causal paths between variables are represented as directed arcs/edges/lines, often in the form of arrows (see Figure 1). Although each arc indicates the presence and direction of a known/presumed/assumed/speculative causal relationship between the two variables concerned, drawing an arc does not require the sign, magnitude, precision or shape of the relationship to be known or declared (Tennant et al., 2021). In this respect, DAGs provide a simple, uncomplicated, accessible and entirely nonparametric approach for postulating causal relationships amongst any variables of interest even when these are uncertain, unknown or entirely speculative (Ellison, 2020). Nonetheless, as a result of the parametric constraints imposed by the presence/absence of possible arcs within any given DAG, these also reflect and support a number of more sophisticated statistical applications which make it possible to use DAGs to inform the design of multivariable statistical models that reflect the causal structure(s) involved – albeit without the need to know or understand the mathematical technicalities on which these are based (Lewis and Kuerbis, 2016). These features make DAGs attractive cognitive, educational and analytical tools for strengthening the epistemological, theoretical and empirical basis of causal inference, and there has been a recent proliferation in the use of DAGs across a range of applied scientific disciplines (e.g. Knight and Winship, 2013), and an associated upsurge in analytical methods training (e.g. Elwert, 2011; Gilthorpe, 2017; Hernán 2018; Roy, 2021; Hünermund, 2021). This Chapter reflects on a decade of delivering medical statistics training to undergraduate medical students at the University of Leeds between 2012-2021 in which the third year research, evaluation and special studies module (‘RESS3’) has used DAGs to support the development of applied statistical skills relevant to the extended student-selected research and evaluation projects (ESREP) students undertake in their fourth and final years (Ellison, 2021; Ellison et al., 2014a,b). Based on successive iterations of the structure and content of the RESS3 module, together with notes made during formal and informal planning and review meetings with module leads, lecturers, tutors and students, we draw on the claims and criticisms made of DAGs in the epidemiological literature to identify a number of explicit strengths (and associated, often implicit. weaknesses) that are central to their use in prediction and causal inference modelling. While using DAGs requires (and benefits from) a clear understanding of their non-parametric nature and parametric implications, the weaknesses of DAGs seem likely to reflect both: the challenges inherent in the modelling of data generating processes when these are imperfectly understood; and troublesome cognitive and heuristic tendencies common to all analytical tools – in which the tool facilitates the task in hand by reducing the necessity (and benefits of) exploring uncertainties and identifying assumptions. These, more epistemological considerations appear particularly challenging for medical undergraduates to grasp (Ellison, 2021), but also appear poorly understood by many established analysts and clinical epidemiologists (Ellison, 2020).

A simple undirected graph $\Gamma=(V_\Gamma,E_\Gamma)$ admits an $H$-covering if every edge in $E_\Gamma$ belongs to at least one subgraph of $\Gamma$ that isomorphic to a graph $H$. For any graph $\Gamma$ admitting $H$-covering, a total Labelling $\beta: V_\Gamma \cup E_\Gamma \longrightarrow \{1,2,\dots,p\}$ is called an $H$-irregular total $p$-labelling of $\Gamma$ if every two different subgraphs $H_1$ and $H_2$ of $\Gamma$ isomorphic to $H$ have distinct weights where the weight $w_\beta(K)$ of subgraph $K$ of $\Gamma$ is defined as $w_f(K):=\displaystyle \sum_{v\in V_K} f(v) + \sum_{e\in E_K} f(e)$. The smallest number $p$ for which a graph $\Gamma$ admits an $H$-irregular total $p$-labelling is called the total $H$-irregularity strength of $\Gamma$ and is denoted by $ths(\Gamma)$. In this paper, we determine the total $H$-irregularity strength of edge comb product of two graphs.

Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.

The chemical graph theory is a subfield of mathematical chemistry which applies classic graph theory to chemical entities and phenomena. Chemical graphs are main data structures to represent chemical structures in cheminformatics. Computable properties of graphs lay the foundation for (quantitative) structure activity and structure property predictions - a core discipline of cheminformatics. It has a historic relevance for natural sciences, such as chemistry, biochemistry and biology, and is in the heart of modern disciplines, such as cheminformatics and bioinformatics. This review first covers the history of chemical graph theory, then provides an overview of its various techniques and applications for CASE, and finally summarises modern tools using chemical graph theory for CASE.

This work presents a multi-start algorithm for solving the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP) allowing for the rotation of goods. Researches dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics such as the Constructive Genetic Algorithm (CGA), to construct promising initial solutions; a Tabu Search (TS), to improve the initial solutions on the routing problem; and a Large Neighborhood Search (LNS), for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multi-threading programming to improve the performance. Additionally, memory structures, like hash-tables, were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest of the community involved in symmetry studies, such as, graph algorithms and graph theory.

Paraphrase generation is an important yet challenging task in NLP. Neural network-based approaches have achieved remarkable success in sequence-to-sequence(seq2seq) learning. Previous paraphrase generation work generally ignores syntactic information regardless of its availability, with the assumption that neural nets could learn such linguistic knowledge implicitly. In this work we make an endeavor to probe into the efficacy of explicit syntactic information for the task of paraphrase generation. Syntactic information can appear in the form of dependency trees which could be easily acquired from off-the-shelf syntactic parsers. Such tree structures could be conveniently encoded via graph convolutional networks(GCNs) to obtain more meaningful sentence representations, which could improve generated paraphrases. Through extensive experiments on four paraphrase datasets with different sizes and genres, we demonstrate the utility of syntactic information in neural paraphrase generation under the framework of seq2seq modeling. Specifically, our GCN-enhanced models consistently outperform their syntax-agnostic counterparts in multiple evaluation metrics.

This paper presents a new framework to classify floor plan elements and represent them in a vector format. Unlike existing approaches using image-based learning frameworks as the first step to segment the image pixels, we first convert the input floor plan image into vector data and utilize graph neural network. Our framework consists of three steps. (1) image pre-processing and vectorization of the floor plan image. (2) region adjacency graph conversion. (3) graph neural network on converted floor plan graphs. Our approach is able to capture different types of indoor elements including basic elements such as walls, doors, and symbols as well as spatial elements such as rooms and corridors. In addition, the proposed method can also detect element shapes. Experimental results show that our framework can classify indoor elements with an F1 score of 95%, with scale and rotation invariance. Furthermore, we propose a new graph neural network model that takes the distance between nodes into account, which is a valuable feature of spatial network data.

Let G be a graph with n vertices and let 1; 2; : : : ; n be the eigenvalues of Randic matrix. The Randic Estrada index of G is REE(G) = Ón i=1 ei . In this paper, we establish lower and upper bounds for Randic index in terms of graph invariants such as the number of vertices and eigenvalues of graphs and improve some previously published lower bounds.