EigenvectorCentrality

EigenvectorCentrality[g]
gives a list of eigenvector centralities for the vertices in the graph g.

EigenvectorCentrality[g, "In"]
gives a list of in-centralities for a directed graph g.

EigenvectorCentrality[g, "Out"]
gives a list of out-centralities for a directed graph g.

Details and OptionsDetails and Options

  • EigenvectorCentrality will give high centralities to vertices that are connected to many other well-connected vertices.
  • EigenvectorCentrality gives a list of centralities that can be expressed as a weighted sum of centralities of its neighbors.
  • With being the largest eigenvalue of the adjacency matrix for the graph g, you have:
  • EigenvectorCentrality[g]c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c
    EigenvectorCentrality[g,"In"]c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c, left eigenvector
    EigenvectorCentrality[g,"Out"], right eigenvector
  • Eigenvector centralities are normalized.
  • For a directed graph g, EigenvectorCentrality[g] is equivalent to EigenvectorCentrality[g, "In"].
  • The option WorkingPrecision->p can be used to control precision used in internal computations.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

Compute eigenvector centralities:

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Highlight:

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Rank the vertices. Highest-ranked vertices are connected to many well-connected vertices:

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