BUILT-IN MATHEMATICA 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, {{vi1, vi2, ...}, ...}]
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 .

## 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, {{vi1, vi2, ...}, ...}], 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 .

## ExamplesExamplesopen allclose all

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

Compute the assortativity coefficient of the Zachary karate club network:

 Out[1]=

Distribution of the assortativity coefficient of uniform random graphs:

 Out[1]=