Comparative analysis of centrality measures of network nodes based on principal component analysis

The analysis of networks of a diverse nature, which are citation networks, social networks or information and communication networks, includes the study of topological properties that allow one to assess the relationships between network nodes and evaluate various characteristics, such as the density and diameter of the network, related subgroups of nodes, etc. For this, the network is represented as a graph – a set of vertices and edges between them. One of the most important tasks of network analysis is to estimate the significance of a node (or in terms of graph theory – a vertex). For this, various measures of centrality have been developed, which make it possible to assess the degree of significance of the nodes of the network graph in the structure of the network under consideration.
The existing variety of measures of centrality gives rise to the problem of choosing the one that most fully describes the significance and centrality of the node.
The relevance of the work is due to the need to analyze the centrality measures to determine the significance of vertices, which is one of the main tasks of studying networks (graphs) in practical applications.
The study made it possible, using the principal component method, to identify collinear measures of centrality, which can be further excluded both to reduce the computational complexity of calculations, which is especially important for networks that include a large number of nodes, and to increase the reliability of the interpretation of the results obtained when evaluating the significance node within the analyzed network in solving practical problems.
In the course of the study, the patterns of representation of various measures of centrality in the space of principal components were revealed, which allow them to be classified in terms of the proximity of the images of network nodes formed in the space determined by the measures of centrality used.