betweenness {igraph} | R Documentation |
The vertex and edge betweenness are (roughly) defined by the number of geodesics (shortest paths) going through a vertex or an edge.
betweenness(graph, v=V(graph), directed = TRUE) edge.betweenness(graph, e=E(graph), directed = TRUE)
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. |
The vertex betweenness of vertex v
is defined
by
sum( g_ivj / g_ij, i!=j,i!=v,j!=v)
The edge betweenness of edge e
is defined by
sum( g_iej / g_ij, i!=j)
.
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.
edge.betweenness
might give false values for graphs with
multiple edges.
Gabor Csardi csardi@rmki.kfki.hu
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.
g <- random.graph.game(10, 3/10) betweenness(g) edge.betweenness(g)