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

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

# GraphAssortativity

gives the assortativity coefficient of a graph g using vertex degrees.

GraphAssortativity[g,"prop"]
gives the assortativity coefficient of the graph g using vertex property .

GraphAssortativity[g,{{vi 1,vi 2,},}]
gives the assortativity coefficient of the graph g with respect to the vertex partition .

GraphAssortativity[g,{v1,v2,}{x1,x2,}]
gives the assortativity coefficient of the graph g using data for vertices .

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

## Details and OptionsDetails and Options

• For a graph with edges and adjacency matrix entries , the assortativity coefficient is given by , where is the out-degree for the vertex and is 1 if there is an edge from to and 0 otherwise.
• For quantitative data where are used, is taken to be .
• For categorical data where are used, is taken to be 1 if and are equal and 0 otherwise.
• In , is taken to be the vertex out-degree for the vertex .
• In GraphAssortativity[g,"prop"], is taken to be PropertyValue[{g,vi},"prop"] for the vertex .
• In GraphAssortativity[g,{{vi 1,vi 2,},}], vertices in a subset have the same categorical data .
• GraphAssortativity[g,Automatic->{x1,x2,}] takes the vertex list to be VertexList[g].
• The option "DataType"->type can be used to specify the type for the data . Possible settings are and .
• The option "Normalized"->False can be used to compute the assortativity modularity.
• For a graph with edges and adjacency matrix entries , the assortativity modularity is given by , where is the out-degree for the vertex .
• GraphAssortativity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

## ExamplesExamplesopen allclose all

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

Compute the assortativity coefficient of the Zachary karate club network:

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Distribution of the assortativity coefficient of uniform random graphs:

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