assortativity#

graph_tool.correlations.assortativity(g, deg, eweight=None)[source]#

Obtain the assortativity coefficient for the given graph.

Parameters:

gGraph: Graph to be used.
degstring or VertexPropertyMap: Degree type (“in”, “out” or “total”) or vertex property map, which specifies the vertex types.
eweightEdgePropertyMap (optional, default: None): If given, this will specify the edge weights, otherwise a constant value of one will be used.

Returns:

assortativity coefficienttuple of two floats: The assortativity coefficient, and its variance.

See also

assortativity: assortativity coefficient
scalar_assortativity: scalar assortativity coefficient
corr_hist: vertex-vertex correlation histogram
combined_corr_hist: combined single-vertex correlation histogram
avg_neighbor_corr: average nearest-neighbor correlation
avg_combined_corr: average combined single-vertex correlation

Notes

The assortativity coefficient [newman-mixing-2003] tells in a concise fashion how vertices of different types are preferentially connected amongst themselves, and is defined by

\[r = \frac{\sum_i e_{ii} - \sum_i a_i b_i}{1-\sum_i a_i b_i}\]

where \(a_i=\sum_je_{ij}\) and \(b_j=\sum_ie_{ij}\), and \(e_{ij}\) is the fraction of edges from a vertex of type i to a vertex of type j.

The variance is obtained with the jackknife method.

Parallel implementation.

If enabled during compilation, this algorithm will run in parallel using OpenMP. See the parallel algorithms section for information about how to control several aspects of parallelization.

References

[newman-mixing-2003]

M. E. J. Newman, “Mixing patterns in networks”, Phys. Rev. E 67, 026126 (2003), DOI: 10.1103/PhysRevE.67.026126 [sci-hub, @tor]

Examples

>>> g = gt.collection.data["pgp-strong-2009"]
>>> g = gt.GraphView(g, directed=False)
>>> gt.assortativity(g, "out")
(0.0240578552..., 0.0003272847...)

assortativity

Contents

assortativity#