EigenvectorCentrality returns the eigenvector centrality for a specified vertex in the given graph G, or if no vertex is specified, returns a list of the eigenvector centralities for each vertex in G.

Let A be the adjacency matrix of G. The eigenvector centrality of a vertex v in G is the normalized value of the corresponding entry in the eigenvector of A which corresponds with the largest eigenvalue of A.

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 8\; edges}$

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

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

$\left[0.130085678713417\,0.149538495378514\,0.130085678713417\,0.187421156483979\,0.149538495378514\,0.253330495332159\right]$

The GraphTheory[EigenvectorCentrality] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.