GraphAssortativity

GraphAssortativity[g]

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 "prop".

GraphAssortativity[g,{{vi 1,vi 2,},}]

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

GraphAssortativity[g,{v1,v2,}{x1,x2,}]

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

GraphAssortativity[{vw,},]

uses rules vw to specify the graph g.

Details 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 vi and is 1 if there is an edge from vi to vj and 0 otherwise.
  • For quantitative data where x1,x2, are used, is taken to be xixj.
  • For categorical data where x1,x2, are used, is taken to be 1 if xi and xj are equal and 0 otherwise.
  • In GraphAssortativity[g], xi is taken to be the vertex out-degree for the vertex vi.
  • In GraphAssortativity[g,"prop"], xi is taken to be PropertyValue[{g,vi},"prop"] for the vertex vi.
  • In GraphAssortativity[g,{{vi 1,vi 2,},}], vertices in a subset {vi 1,vi 2,} have the same categorical data xi 1=xi 2=.
  • 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 x1,x2,. Possible settings are "Quantitative" and "Categorical".
  • 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 vi.
  • GraphAssortativity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

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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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Scope  (12)

Applications  (3)

Properties & Relations  (2)

See Also

MeanDegreeConnectivity  Correlation

Introduced in 2012
(9.0)
| Updated in 2015
(10.3)