Localization and centrality in networks

2014/01/31 by Travis Martin, Xiao Zhang, M. E. J. Newman · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Betweenness centrality #Centrality #Combinatorics #Complex Network Analysis Techniques #Computer science #Data mining #Eigenvalues and eigenvectors #Graph theory and applications #Katz centrality #Mathematics #Measure (data warehouse) #Metric (unit) #Network theory #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #cond-mat.stat-mech #cs.SI #physics.soc-ph

paper · pdf · doi:10.1103/physreve.90.052808

published as Phys. Rev. E 90, 052808 (2014) · 5 pages, 1 figure

openalex publication_date 2014/11/12 · arxiv created 2015/01/03 · arxiv updated 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails.

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