EdgeBetweennessCentrality

EdgeBetweennessCentrality[g]
gives a list of betweenness centralities for the edges in the graph g.

DetailsDetails

  • The edge betweenness centrality of an edge is the number of shortest paths between pairs of vertices that run along it.
  • EdgeBetweennessCentrality works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Background
Background

  • EdgeBetweennessCentrality returns a list of positive machine numbers ("edge betweenness centralities") that approximate particular centrality measures of the edges of a graph. For graphs on one or more edges, edge betweenness centralities lie between and 2TemplateBox[{{{n, ^, 2}, /, 4}}, Floor] inclusive. Edge betweenness centrality is a measure of centrality of an edge in a network based on the number of shortest paths that pass through the given edge. It therefore identifies edges in the network that are crucial for information flows. This measure has found applications in social networks, transportation, biology, and social sciences.
  • The edge betweenness centrality of an edge is the number of shortest paths between pairs of vertices that run along it.
  • BetweennessCentrality applies the same betweenness concept to find the node-based betweenness centrality.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Compute edge betweenness centralities:

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Highlight:

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Rank edges. Highest-ranked edges are on many shortest paths of pairs of vertices:

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Introduced in 2012
(9.0)
| Updated in 2014
(10.0)