The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Localization and centrality in networks
Open accessAbstract
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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Citations
Cites
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Social Network Analysis: Methods and Applications
Wasserman, S., & Faust, K. (1994) · doi:10.1017/cbo9780511815478 · Cited by 17,557
The anatomy of a large-scale hypertextual Web search engine
Brin, S., & Page, L. (1998) · Computer Networks and ISDN Systems · doi:10.1016/s0169-7552(98)00110-x · Cited by 16,004
Size-dependent degree distribution of a scale-free growing network
Dorogovtsev, S. N., Mendes, J. F. F., & Samukhin, A. N. (2001) · Physical Review E · doi:10.1103/physreve.63.062101 · Cited by 311 · cited 1×
“(cid:10) (cid:11) h i In a power-law network with n vertices and exponent α , the highest degree goes as d ∼ n 1 / ( α − 1) [17] and hence increases with increasing n , while (cid:10) k 2 (cid:11) ∼ d 3 − α and h k i ∼ constant for the common case of α < 3.”
Background
Cited by
Epidemic processes in complex networks
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.925 · Cited by 3,697
Random walks and diffusion on networks
Masuda, N., Porter, M. A., & Lambiotte, R. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.07.007 · Cited by 657
Opinion Dynamics and the Evolution of Social Power in Influence Networks
Jia, P., MirTabatabaei, A., Friedkin, N. E., & Bullo, F. (2015) · SIAM Review · doi:10.1137/130913250 · Cited by 318
Metadata
- Authors
- Martin, T., Zhang, X., & Newman, M. E. J.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2014-11-12
- Volume
- 90
- Issue
- 5
- Pages
- 052808-052808
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2058526570
- Cited by
- 309
- References
- 4
- FWCI
- 11.21
- Type
- journal article
- Language
- en
- Open access
- green
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- Martin, T., Zhang, X., & Newman, M. E. J. (2014). Localization and centrality in networks. Physical Review E. https://doi.org/10.1103/physreve.90.052808
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