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, verbose = igraph.par("verbose")) edge.betweenness(graph, e=E(graph), directed = TRUE) betweenness.estimate(graph, vids = V(graph), directed = TRUE, cutoff, verbose = igraph.par("verbose")) edge.betweenness.estimate(graph, directed = TRUE, cutoff)
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. |
verbose |
Logical, whether to show a progress bar. |
vids |
The vertices for which the vertex betweenness estimation will be calculated. |
cutoff |
The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit. |
The vertex betweenness of vertex \code{v} is defined by
sum( g_ivj / g_ij, i!=j,i!=v,j!=v)
The edge betweenness of edge \code{e} is defined by
sum( g_iej / g_ij, i!=j)
.
betweenness
calculates vertex betweenness,
edge.betweenness
calculates edge.betweenness.
betweenness.estimate
only considers paths of length
cutoff
or smaller, this can be run for larger graphs, as the
running time is not quadratic (if cutoff
is small). If
cutoff
is zero or negative then the function calculates the
exact betweenness scores.
edge.betweenness.estimate
is similar, but for edges.
For calculating the betweenness a similar algorithm to the one proposed by Brandes (see References) is used.
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
.
betweenness.estimate
returns the estimated betweenness scores
for vertices in vids
, edge.betweenness.estimate
the estimated edge betweenness score for all edges; both in
a numeric vector.
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)