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 :

G : NetworkX 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 :

r : float

Assortativity of graph by degree.

See also

attribute_assortativity_coefficient, numeric_assortativity_coefficient, neighbor_connectivity, degree_mixing_dict, degree_mixing_matrix

Notes

This computes Eq. (21) in Ref. [R97] , 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

[R97]

(1, 2) M. E. J. Newman, Mixing patterns in networks, Physical Review E, 67 026126, 2003

[R98]

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("%3.1f"%r)
-0.5