networkx.algorithms.assortativity.attribute_mixing_matrix

attribute_mixing_matrix(G, attribute, nodes=None, mapping=None, normalized=True)[source]

Returns mixing matrix for attribute.

Parameters
Ggraph

NetworkX graph object.

attributestring

Node attribute key.

nodes: list or iterable (optional)

Use only nodes in container to build the matrix. The default is all nodes.

mappingdictionary, optional

Mapping from node attribute to integer index in matrix. If not specified, an arbitrary ordering will be used.

normalizedbool (default=True)

Return counts if False or probabilities if True.

Returns
m: numpy array

Counts or joint probability of occurrence of attribute pairs.

Notes

If each node has a unique attribute value, the unnormalized mixing matrix will be equal to the adjacency matrix. To get a denser mixing matrix, the rounding can be performed to form groups of nodes with equal values. For example, the exact height of persons in cm (180.79155222, 163.9080892, 163.30095355, 167.99016217, 168.21590163, …) can be rounded to (180, 163, 163, 168, 168, …).

Definitions of attribute mixing matrix vary on whether the matrix should include rows for attribute values that don’t arise. Here we do not include such empty-rows. But you can force them to appear by inputting a mapping that includes those values.

Examples

>>> G = nx.path_graph(3)
>>> gender = {0: 'male', 1: 'female', 2: 'female'}
>>> nx.set_node_attributes(G, gender, 'gender')
>>> mapping = {'male': 0, 'female': 1}
>>> mix_mat = nx.attribute_mixing_matrix(G, 'gender', mapping=mapping)
>>> # mixing from male nodes to female nodes
>>> mix_mat[mapping['male'], mapping['female']]
0.25