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A measure of betweenness centrality based on random walks
Abstract
Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here, we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks.
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Cites
Centrality in social networks conceptual clarification
Freeman, L. C. (1978) · Social Networks · doi:10.1016/0378-8733(78)90021-7 · Cited by 17,062
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931
Self-citation
Cited by
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Borgatti, S. P. (2005) · Social Networks · doi:10.1016/j.socnet.2004.11.008 · Cited by 3,191
Random Walks for Image Segmentation
Grady, L. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.233 · Cited by 2,624
Graph embedding techniques, applications, and performance: A survey
Goyal, P., & Ferrara, E. (2018) · Knowledge-Based Systems · doi:10.1016/j.knosys.2018.03.022 · Cited by 1,801
Fouss, F., Pirotte, A., Renders, J.-M., & Saerens, M. (2007) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2007.46 · Cited by 1,265
Metadata
- Authors
- Newman, M. E. J.
- Venue
- Social Networks
- Publisher
- Elsevier BV
- Published
- 2005-01
- Volume
- 27
- Issue
- 1
- Pages
- 39-54
- ISSN
- 0378-8733 (ISSN-L)
- OpenAlex
- W2154897810
- Cited by
- 2,461
- References
- 2
- FWCI
- 23.88
- Type
- journal article
- Language
- en
- Open access
- closed
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