# betweenness

0th

Percentile

##### Vertex and edge betweenness centrality

The vertex and edge betweenness are (roughly) defined by the number of geodesics (shortest paths) going through a vertex or an edge.

Keywords
graphs
##### Usage
betweenness(graph, v=V(graph), directed = TRUE)
edge.betweenness(graph, e=E(graph), directed = TRUE)
##### Arguments
graph
The graph to analyze.
v
The vertices for which the vertex betweenness will be calculated.
e
The edges for which the edge betweenness will be calculated.
directed
Logical, whether directed paths should be considered while determining the shortest paths.
##### Details

The vertex betweenness of vertex $v$ is defined by

$$\sum_{i\ne j, i\ne v, j\ne v} g_{ivj}/g_{ij}$$ The edge betweenness of edge $e$ is defined by

$$\sum_{i\ne j} g{iej}/g_{ij}$$.

##### Value

• A numeric vector with the betweenness score for each vertex in v for betweenness.

A numeric vector with the edge betweenness score for each edge in e for edge.betweenness.

For calculating the betweenness a similar algorithm to the one proposed by Brandes is used.

##### Note

edge.betweenness might give false values for graphs with multiple edges.

##### References

Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.

Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001.

closeness, degree

##### Aliases
• betweenness
• edge.betweenness
##### Examples
g <- random.graph.game(10, 3/10)
betweenness(g)
edge.betweenness(g)
Documentation reproduced from package igraph, version 0.4.4, License: GPL version 2 or later (June, 1991)

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