EigenvectorCentrality - Maple Help

GraphTheory

 EigenvectorCentrality
 compute eigenvector centrality

 Calling Sequence EigenvectorCentrality(G) EigenvectorCentrality(G, v)

Parameters

 G - graph v - (optional) a vertex of G

Description

 • 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.

Examples

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

Compute the eigenvector centrality for a specified graph.

 > $G≔\mathrm{Graph}\left(6,\left\{\left\{1,3\right\},\left\{1,6\right\},\left\{2,6\right\},\left\{2,4\right\},\left\{3,6\right\},\left\{4,6\right\},\left\{4,5\right\},\left\{5,6\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected graph with 6 vertices and 8 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{EigenvectorCentrality}\left(G\right)$
 $\left[{0.130085678713417}{,}{0.149538495378514}{,}{0.130085678713417}{,}{0.187421156483979}{,}{0.149538495378514}{,}{0.253330495332159}\right]$ (2)

Compatibility

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