Centrality metrics and localization in core-periphery networks

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.

15 pages, 8 figures

References in corpus (7)

• Stochastic blockmodels and community structure in networks
• Phase transition in the detection of modules in sparse networks
• Graph spectra and the detectability of community structure in networks
• Core-periphery organization of complex networks
• Parsimonious module inference in large networks
• Identification of core-periphery structure in networks
• A Fast Algorithm for the Discrete Core/Periphery Bipartitioning Problem

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• Principal eigenvector localization and centrality in networks: revisited
• Optimal information diffusion in stochastic block models
• Double phase transition of the Ising model in core-periphery networks
• Heterogenous criticality in high frequency finance: a phase transition in flash crashes
• Centralities in complex networks
• Informative core identification in complex networks
• Spectral density of equitable core-periphery graphs