# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# KatzCentrality

KatzCentrality[g,α]
gives a list of Katz centralities for the vertices in the graph g and weight α.

KatzCentrality[g,α,β]
gives a list of Katz centralities using weight α and initial centralities β.

KatzCentrality[{vw,},]
uses rules to specify the graph g.

## Details and OptionsDetails and Options

• KatzCentrality gives a list of centralities that satisfy , where is the adjacency matrix of g.
• If β is a scalar, it is taken to mean .
• KatzCentrality[g,α] is equivalent to KatzCentrality[g,α,1].
• The option can be used to control the precision used in internal computations.
• KatzCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

## ExamplesExamplesopen allclose all

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

Compute Katz centralities:

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Highlight:

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Rank vertices by centrality; higher value means more influence:

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