BUILT-IN MATHEMATICA SYMBOL

# EigenvectorCentrality

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] EigenvectorCentrality[g,"In"] , left eigenvector EigenvectorCentrality[g,"Out"] , right eigenvector
• Eigenvector centralities are normalized.
• For a directed graph g, is equivalent to EigenvectorCentrality[g, "In"].
• The option can be used to control precision used in internal computations.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Compute eigenvector centralities:

 Out[2]=

Highlight:

 Out[3]=

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

 Out[2]=