LocalClusteringCoefficient returns the local clustering coefficient for a specified vertex in the given graph G, or if no vertex is specified, a list of the coefficients for each vertex in G.

The local clustering coefficient is a number between 0 and 1 measuring how close the neighborhood of v is to a clique.

For a node v with n neighbors, the local cluster coefficient is the number of edges between neighbors of v (counting undirected edges twice) and the number $n\left(n-1\right)$, which is the maximum number of (directed) edges possible between n neighbors.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$G≔\mathrm{Graph}\left(\left[1\,2\,3\,4\,5\,6\right]\,\left\{\left\{1\,3\right\}\,\left\{1\,6\right\}\,\left\{2\,6\right\}\,\left\{2\,4\right\}\,\left\{3\,6\right\}\,\left\{4\,6\right\}\,\left\{4\,5\right\}\,\left\{5\,6\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{LocalClusteringCoefficient}\left(G\,6\right)$

$\frac{3}{10}$

$\mathrm{LocalClusteringCoefficient}\left(G\right)$

$\left[1\,1\,1\,\frac{2}{3}\,1\,\frac{3}{10}\right]$

The GraphTheory[LocalClusteringCoefficient] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.