Title: Assortativity analysis of complex real-world networks using the principal components of the centrality metrics

Authors: Natarajan Meghanathan

Addresses: Department of ECE & CS, Jackson State University, Jackson, MS, Mailbox 18839, USA

Abstract: Principal component analysis (PCA) captures the variations in the data spread over m features into n dominating principal components (typically, n < m, if the features are correlated) that are orthogonal to each other. Assortativity analysis for complex networks has been so far conducted just with the degree centrality metric or some node-level metric of interest, but not with respect to more than one metric. In this paper, we show that PCA can be used to determine the assortativity index (AI) of complex real-world networks with respect to the four major centrality metrics (degree, eigenvector, betweenness, and closeness) considered together (as features representing the data) for the nodes. Assortativity index of the network is computed as the weighted average (AI_PC^w.avg) of the assortativity indices of the network with respect to each principal component, and the weights are the eigenvalues of the eigenvectors corresponding to the principal components.

Keywords: PCA; principal component analysis; assortativity index; centrality metrics; degree centrality; real-world networks.

DOI: 10.1504/IJDS.2024.135945

International Journal of Data Science, 2024 Vol.9 No.1, pp.79 - 97

Received: 07 Oct 2022
Accepted: 30 Jun 2023
Published online: 10 Jan 2024 *

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