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

PageRank centrality computes the relative influence of a vertex within a network by counting the number of immediate neighbors and the total number of reachable vertices. Connections to distant vertices are penalized by an attenuation factor alpha.

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

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

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

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

$\mathrm{PageRankCentrality}\left(G\,0.1\right)$

$\left[0.161848054511877\,0.159412214226581\,0.161848054511877\,0.169696873208941\,0.159412214226581\,0.187782589314144\right]$

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

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