attribute_assortativity_coefficient

attribute_assortativity_coefficient(G, attribute, nodes=None)

Compute assortativity for node attributes.

Assortativity measures the similarity of connections in the graph with respect to the given attribute.

Parameters:

GNetworkX graph

attributestring

Node attribute key

nodes: list or iterable (optional)

Compute attribute assortativity for nodes in container. The default is all nodes.

Returns:

r: float

Assortativity of graph for given attribute

Notes

This computes Eq. (2) in Ref. [1] , (trace(M)-sum(M^2))/(1-sum(M^2)), where M is the joint probability distribution (mixing matrix) of the specified attribute.

References

[1]

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

Examples

>>> G = nx.Graph()
>>> G.add_nodes_from([0, 1], color="red")
>>> G.add_nodes_from([2, 3], color="blue")
>>> G.add_edges_from([(0, 1), (2, 3)])
>>> print(nx.attribute_assortativity_coefficient(G, "color"))
1.0