Centrality metrics and localization in core-periphery networks

TL;DR

This paper explores the relationship between node centrality metrics and the core-periphery structure in networks, finding that belief propagation marginals, PageRank, and degree centrality best identify core nodes.

Contribution

It evaluates the effectiveness of various centrality metrics in detecting core nodes within networks exhibiting strong core-periphery structures, using stochastic block models.

Findings

Belief propagation marginals, PageRank, and degree centrality outperform other metrics.

Non-backtracking and eigenvector centrality perform worse in core detection.

Results are based on networks generated via stochastic block models with strong core-periphery features.

Abstract

Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to a large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connected periphery. In this paper we investigate the relation between these two concepts. We consider networks generated via the Stochastic Block Model, or its degree corrected version, with a strong core-periphery structure and we investigate the centrality properties of the core nodes and the ability of several centrality metrics to identify them. We find that the three measures with the best performance are marginals obtained with belief propagation, PageRank, and degree centrality, while non-backtracking and eigenvector centrality (or MINRES}, showed to be equivalent to the latter in the large network limit) perform worse in the investigated networks.