Use this if you are using igraph from R
The vertex and edge betweenness are (roughly) defined by the number of geodesics (shortest paths) going through a vertex or an edge.
estimate_betweenness( graph, vids = V(graph), directed = TRUE, cutoff, weights = NULL, nobigint = TRUE ) betweenness( graph, v = V(graph), directed = TRUE, weights = NULL, nobigint = TRUE, normalized = FALSE, cutoff = -1 ) edge_betweenness( graph, e = E(graph), directed = TRUE, weights = NULL, cutoff = -1 )
graph |
The graph to analyze. |
vids |
The vertices for which the vertex betweenness estimation will be calculated. |
directed |
Logical, whether directed paths should be considered while determining the shortest paths. |
cutoff |
The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit. |
weights |
Optional positive weight vector for calculating weighted
betweenness. If the graph has a |
nobigint |
Logical scalar, whether to use big integers during the calculation. Deprecated since igraph 1.3 and will be removed in igraph 1.4. |
v |
The vertices for which the vertex betweenness will be calculated. |
normalized |
Logical scalar, whether to normalize the betweenness
scores. If Bnorm=2*B/((n-1)*(n-2)), where Bnorm is the normalized, B the raw betweenness, and n is the number of vertices in the graph. |
e |
The edges for which the edge betweenness will be calculated. |
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).
betweenness
calculates vertex betweenness, edge_betweenness
calculates edge betweenness.
Both functions allow you to consider only 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. Using zero as a
cutoff is deprecated and future versions (from 1.4.0) will treat zero
cutoff literally (i.e. no paths considered at all). If you want no cutoff,
use a negative number.
estimate_betweenness
and estimate_edge_betweenness
are
aliases for betweenness
and edge_betweenness
, with a different
argument order, for sake of compatibility with older versions of igraph.
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
.
edge_betweenness
might give false values for graphs with
multiple edges.
Gabor Csardi csardi.gabor@gmail.com
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
, harmonic_centrality
g <- sample_gnp(10, 3/10) betweenness(g) edge_betweenness(g)