EdgeBetweennessCentrality

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

EdgeBetweennessCentrality[{vw,}]

uses rules vw to specify the graph g.

Details

• 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 & Context

• 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 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.
• For a connected graph, let denote the number of shortest paths between vertices and , and let denote the number of shortest paths between and that go through the edge . Then the edge betweenness centrality of edge is defined as .
• BetweennessCentrality applies the same betweenness concept to find the vertex-based betweenness centrality.

Examples

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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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