Journal
PHYSICAL REVIEW E
Volume 90, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.90.052808
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Funding
- National Science Foundation [DMS-1107796, DMS-1407207]
- Air Force Office of Scientific Research (AFOSR)
- Defense Advanced Research Projects Agency (DARPA) [FA9550-12-1-0432]
- Direct For Mathematical & Physical Scien [1107796] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1107796] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1407207] Funding Source: National Science Foundation
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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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