Three computer algorithms are presented. One reduces a network $\CALN$ to its interior, $\CALI$. Another counts all the triangles in the network, and the last randomly generates networks similar to $\CALN$ given just its interior $\CALI$. But these algorithms are not the usual numeric programs that manipulate a matrix representation of the network; they are set-based. Union and meet are essential binary operators; contained_in is the basic relational comparator. The interior $\CALI$ is shown to have desirable formal properties and to provide an effective way of revealing ``communities'' in social networks.

Abstract Big datasets are becoming increasingly common and can be challenging to understand and apply in public health. One method for lowering the dimensionality of these datasets and improving interpretability while minimizing information loss is data reduction using principal component analysis (PCA). It achieves this by successively maximizing variance through the creation of new, uncorrelated variables. PCA is an adaptive data analysis technique because it simplifies the process of finding new variables, or principal components, by solving an eigenvalue or eigenvector problem. These new variables are determined by the dataset being used, rather than by the analyst starting from scratch. It is also adaptable in another way because varieties of the method have been designed to adjust to various data structures and types. However, there are serious problems in the theoretical understanding and practical application of PCA in public health researchers, whereas its application is becoming popular in developing countries. Therefore, this article, which concentrated on using PCA to reduce data, began by outlining the fundamental concepts of PCA and going over what it can and cannot do, as well as when and how to use it. We also discussed the fundamental assumptions, benefits, and drawbacks of PCA. Furthermore, this article demonstrated and resolved PCA practical application problems in public health that most scholars are unaware of, such as variable preparation, variable inclusion and exclusion criteria for PCA, iteration steps, wealth index analysis, interpretation, and ranking.