  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.
