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BUILT-IN MATHEMATICA SYMBOL
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 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](Files/EigenvectorCentrality.en/4.png "c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c")
EigenvectorCentrality[g,"In"] ![c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c](Files/EigenvectorCentrality.en/5.png "c=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].c")
, 
left eigenvectorEigenvectorCentrality[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.
New in 8 | Last modified in 9
