Core-Intermediate-Peripheral Index: Factor Analysis of Neighborhood and Shortest Paths-based Centrality Metrics

Abstract: We perform factor analysis on the raw data of the four major neighborhood and shortest paths-based centrality metrics (Degree, Eigenvector, Betweeenness and Closeness) and propose a novel quantitative measure called the Core-Intermediate-Peripheral (CIP) Index to capture the extent with which a node could play the role of a core node (nodes at the center of a network with larger values for any centrality metric) vis-a-vis a peripheral node (nodes that exist at the periphery of a network with lower values for any centrality metric). We conduct factor analysis (varimax-based rotation of the Eigenvectors) on the transpose matrix of the raw centrality metrics dataset, with the node ids as features, under the hypothesis that there are two factors (core and peripheral) that drive the values incurred by the nodes with respect to the centrality metrics. We test our approach on a diverse suite of 12 complex real-world networks.