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Localization and centrality in networks
Travis Martin1, Xiao Zhang2, M E J Newman3
1Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
Summary
Eigenvector centrality can fail in networks, concentrating importance on a few nodes. A new nonbacktracking matrix centrality measure offers a robust alternative, providing useful network insights where others falter.
Area of Science:
- Network Science
- Graph Theory
- Data Analysis
Background:
- Eigenvector centrality is a standard metric for identifying influential nodes in complex networks.
- However, it can exhibit a localization transition, impairing its utility in certain network structures.
Purpose of the Study:
- To address the limitations of eigenvector centrality.
- To introduce a more robust network centrality measure.
Main Methods:
- Analysis of eigenvector centrality's localization transition.
- Development and application of a novel centrality measure based on the nonbacktracking matrix.
Main Results:
- Demonstrated that eigenvector centrality concentrates weight on a few nodes, reducing its effectiveness.
- The nonbacktracking matrix centrality measure closely mimics eigenvector centrality in dense networks.
- The proposed measure successfully avoids localization and provides useful results in sparse networks.
Conclusions:
- Eigenvector centrality's localization transition limits its application in network analysis.
- Nonbacktracking matrix centrality offers a superior alternative, maintaining efficacy across diverse network densities.
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