PageRankCentrality - Maple Help

GraphTheory

 PageRankCentrality
 compute PageRank centrality

 Calling Sequence PageRankCentrality(G, alpha, ) PageRankCentrality(G, alpha, v)

Parameters

 G - graph alpha - real constant v - (optional) a vertex of G

Description

 • 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.

Examples

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

Compute the PageRank centrality for a specified graph.

 > $G≔\mathrm{Graph}\left(6,\left\{\left\{1,3\right\},\left\{1,6\right\},\left\{2,4\right\},\left\{2,6\right\},\left\{3,6\right\},\left\{4,5\right\},\left\{4,6\right\},\left\{5,6\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 6 vertices and 8 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{PageRankCentrality}\left(G,0.1\right)$
 $\left[{0.161848054511877}{,}{0.159412214226581}{,}{0.161848054511877}{,}{0.169696873208941}{,}{0.159412214226581}{,}{0.187782589314144}\right]$ (2)

Compatibility

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