Compute edge betweenness centralities:

Highlight:

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

EdgeBetweennessCentrality works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

EdgeBetweennessCentrality works with large graphs:

Rank the edges of a graph by the number of shortest paths that run along them:

Highlight the edge betweenness centrality for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

A road network linking Chicago suburbs. Find the most central roads, assuming that Chicago residents use the shortest routes to travel:

The two roads that are part of most shortest paths:

A power grid network representing the topology of the Western States Power Grid of the United States. Identify sections of the grid that may carry the most load:

A view of the critical sections:

A metabolic cellular network for Mycobacterium bovis. The frequency of the edge betweenness centrality has a Poisson-like distribution with a very sharp spike:

Obtain the maximum likelihood parameter estimates:

Edge betweenness centralities for an undirected graph are equivalent to centralities for each component:

Computing the centralities for each component yields the same result:

Use EdgeIndex to obtain the centrality of a specific vertex: