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BUILT-IN MATHEMATICA SYMBOL
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 
.
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 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 GraphAssortativity[g],
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 
.
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