scalar_assortativity#

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

Obtain the scalar 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 scalar values.
eweightEdgePropertyMap (optional, default: None): If given, this will specify the edge weights, otherwise a constant value of one will be used.

Returns:

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

\[r = \frac{\sum_{xy} xy(e_{xy} - a_x b_y)}{\sigma_a\sigma_b}\]

where \(a_x=\sum_ye_{xy}\) and \(b_y=\sum_xe_{xy}\), and \(e_{xy}\) is the fraction of edges from a vertex of type x to a vertex of type y.

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.scalar_assortativity(g, "out")
(0.026384932418..., 0.001213444270...)

scalar_assortativity

Contents

scalar_assortativity#