The heterogeneous structure implies that a few nodes may be crucial in maintaining network structural and functional properties. Identifying these crucial nodes correctly and quickly is a primary issue as contemporarily may face the mushrooming of large-scale datasets. Besides, the ‘weight issue’ is always ignored in this field which edge weight may play a positive/negative role in contributing to the node importance in different weighted networks. This paper provides a novel algorithm, Weighted Expectation Algorithm (WEA), which aims to ensure accuracy and speed of computation by taking advantage of dynamic programming to better handle the task of large-scale networks. Additionally, the weight issue that edge weights may contribute differently is addressed by a simply quantitative definition. Two standard experiments show WEA can maintain the network structure in connectivity well (by the lowest average robustness 0.192) and identify the node importance better in the spreading function test of spreading dynamics (by the highest average Kendall’s tau-b 0.678). In addition, the time complexities of different algo-rithms are evaluated, and their time-consuming are tested, proving that WEA consumes a rela-tively short time.

Intrinsically Disordered Proteins (IDPs) play crucial roles in signal transduction, cell differentiation, and transcriptional regulation. Many disrupted genes associated with mental disorders are identified as IDPs, and emerging evidence suggests the functional role of IDPs in neuropsychiatric disorders. However, few studies comprehensively explore the functional association between protein disorder properties and different mental diseases. To address this gap, we collected disrupted gene sets for seven mental diseases (MDD, SCZ, BP, ID, AD, ADHD, ASD) and a control gene set from normal brains using DisGeNET and GeneCards databases. The state-of-the-art predictor IUPred2A was then utilized to calculate the disorder properties , followed by a thorough comparison between the disordered proteins in mental diseases and healthy controls. Functional enrichment analysis and protein-protein interaction networks were conducted to investigate the IDPs’ functional roles in psychiatric diseases. Additionally, we demonstrated the role of IDPs in protein binding formations through a case study of alpha-synuclein using protein docking. Our findings reveal that differentially expressed proteins in mental disorders, especially in ASD and ADHD, exhibit more IDPs than those in healthy controls. IDPs in psychiatric disorders are significantly enriched in neurodevelopmental pathways and play an important role in in gene expression regulation. Our results indicate distinct functional patterns of disorder proteins among mental diseases and healthy controls. When comparing the IDPs between ASD and ADHD, we observed that IDPs in ADHD are more likely linked to the synaptic signaling and regulation, while IDPs in ASD are more tendentiously related to diverse and complex biological processes. Our work offers valuable insights into the important functions of IDPs in psychiatric disorders, enhancing our understanding of the molecular mechanisms involved in psychiatric disorders.