Spectral centrality measures in complex networks

TL;DR

This paper reviews and compares spectral centrality measures like PageRank, eigenvector centrality, and HITS scores in complex networks, highlighting their relations and differences in node importance ranking.

Contribution

It provides a comparative analysis of spectral centrality measures and derives relations between these measures and node degrees in certain limits.

Findings

PageRank, eigenvector centrality, and HITS scores are related to node degrees.

Different spectral measures can produce varying node rankings.

Relations between measures and degrees are derived in specific limits.

Abstract

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.