betweenness  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,
weights = NULL,
normalized = FALSE,
cutoff = 1
)
edge_betweenness(
graph,
e = E(graph),
directed = TRUE,
weights = NULL,
cutoff = 1
)
graph 
The graph to analyze. 
v 
The vertices for which the vertex betweenness will be calculated. 
directed 
Logical, whether directed paths should be considered while determining the shortest paths. 
weights 
Optional positive weight vector for calculating weighted
betweenness. If the graph has a 
normalized 
Logical scalar, whether to normalize the betweenness
scores. If
where

cutoff 
The maximum shortest path length to consider when calculating betweenness. If negative, then there is no such limit. 
e 
The edges for which the edge betweenness will be calculated. 
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}.
betweenness()
calculates vertex betweenness, edge_betweenness()
calculates edge betweenness.
Here g_{ij}
is the total number of shortest paths between vertices
i
and j
while g_{ivj}
is the number of those shortest paths
which pass though vertex v
.
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 negative (the default),
then the function calculates the exact betweenness scores. Since igraph 1.6.0,
a cutoff
value of zero is treated literally, i.e. paths of length larger
than zero are ignored.
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, 215239. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/03788733(78)900217")}
Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163177, 2001. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/0022250X.2001.9990249")}
closeness()
, degree()
, harmonic_centrality()
Centrality measures
alpha_centrality()
,
authority_score()
,
closeness()
,
diversity()
,
eigen_centrality()
,
harmonic_centrality()
,
hits_scores()
,
page_rank()
,
power_centrality()
,
spectrum()
,
strength()
,
subgraph_centrality()
g < sample_gnp(10, 3 / 10)
betweenness(g)
edge_betweenness(g)
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