GraphTheory
BetweennessCentrality
compute betweenness centrality
Calling Sequence
Parameters
Description
Examples
Compatibility
BetweennessCentrality(G)
BetweennessCentrality(G, v)
G

graph
v
(optional) a vertex of G
BetweennessCentrality returns the betweenness centrality for a specified vertex in the given graph G, or if no vertex is specified, returns a list of the betweenness centralities for each vertex in G.
The betweenness centrality of a vertex v is a measure of the proportion of shortest paths through the graph which pass through v. It is the sum over all pairs of vertices a and b (both different from v) of the number of leastweight paths from a to b which pass through v divided by the total number of leastweight paths from a to b.
$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$
Compute the betweenness centrality for a specified graph.
$G\u2254\mathrm{Graph}\left(6\,\left\{\left\{1\,3\right\}\,\left\{1\,6\right\}\,\left\{2\,4\right\}\,\left\{2\,6\right\}\,\left\{3\,6\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\right\}\right)$
${G}{\u2254}{\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}}$
$\mathrm{DrawGraph}\left(G\right)$
$\mathrm{BetweennessCentrality}\left(G\,6\right)$
$\frac{{13}}{{2}}$
$\mathrm{BetweennessCentrality}\left(G\right)$
$\left[{0}{\,}{0}{\,}{0}{\,}\frac{{1}}{{2}}{\,}{0}{\,}\frac{{13}}{{2}}\right]$
The GraphTheory[BetweennessCentrality] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
See Also
ClosenessCentrality
DegreeCentrality
EigenvectorCentrality
HarmonicCentrality
InformationCentrality
KatzCentrality
PageRankCentrality
Download Help Document
What kind of issue would you like to report? (Optional)