degree_assortativity_coefficient

degree_assortativity_coefficient(G, x='out', y='in', weight=None, nodes=None)

Compute degree assortativity of graph.

Assortativity measures the similarity of connections in the graph with respect to the node degree.

Parameters

GNetworkX graph

x: string (‘in’,’out’)

The degree type for source node (directed graphs only).

y: string (‘in’,’out’)

The degree type for target node (directed graphs only).

weight: string or None, optional (default=None)

The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

nodes: list or iterable (optional)

Compute degree assortativity only for nodes in container. The default is all nodes.

Returns

rfloat

Assortativity of graph by degree.

See also

attribute_assortativity_coefficient

numeric_assortativity_coefficient

degree_mixing_dict

degree_mixing_matrix

Notes

This computes Eq. (21) in Ref. [1] , where e is the joint probability distribution (mixing matrix) of the degrees. If G is directed than the matrix e is the joint probability of the user-specified degree type for the source and target.

References

1

M. E. J. Newman, Mixing patterns in networks, Physical Review E, 67 026126, 2003

2

Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M. Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).

Examples

>>> G = nx.path_graph(4)
>>> r = nx.degree_assortativity_coefficient(G)
>>> print(f"{r:3.1f}")
-0.5