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)
edge_betweenness(graph, e = E(graph), directed = TRUE, weights = NULL)
weight
edge attribute, then this is
used by default.TRUE
(the
default), then big integers are not used.TRUE
, then the results are normalized according to
$$B^n=\frac{2B}{n^2-3n+2}$$, where
$B^n$ is the normalized, $B$ the raw betweenness, and $n$
is the number of vertices in the gv
for betweenness
.A numeric vector with the edge betweenness score for each edge in e
for edge_betweenness
.
estimate_betweenness
returns the estimated betweenness scores for
vertices in vids
, estimate_edge_betweenness
the estimated edge
betweenness score for all edges; both in a numeric vector.
$$\sum_{i\ne j, i\ne v, j\ne v} g_{ivj}/g_{ij}$$
The edge betweenness of edge $e$ is defined by
$$\sum_{i\ne j} g{iej}/g_{ij}.$$
betweenness
calculates vertex betweenness, edge_betweenness
calculates edge betweenness.
estimate_betweenness
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.
estimate_edge_betweenness
is similar, but for edges.
For calculating the betweenness a similar algorithm to the one proposed by Brandes (see References) is used.
Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001.
closeness
, degree
g <- sample_gnp(10, 3/10)
betweenness(g)
edge_betweenness(g)
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