gives a list of betweenness centralities for the vertices in the graph g.
uses rules vw to specify the graph g.
- BetweennessCentrality will give high centralities to vertices that are on many shortest paths of other vertex pairs.
- BetweennessCentrality for a vertex in a connected graph is given by , where is the number of shortest paths from to and is the number of shortest paths from to passing through .
- The ratio is taken to be zero when there is no path from to .
- BetweennessCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examplesopen allclose all
Basic Examples (2)
Highlight the betweenness centrality for CycleGraph:
Properties & Relations (3)
Use VertexIndex to obtain the centrality of a specific vertex:
Wolfram Research (2010), BetweennessCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/BetweennessCentrality.html (updated 2015).
Wolfram Language. 2010. "BetweennessCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/BetweennessCentrality.html.
Wolfram Language. (2010). BetweennessCentrality. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BetweennessCentrality.html