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 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 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.

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