degree_mixing_matrix#

degree_mixing_matrix(G, x='out', y='in', weight=None, nodes=None, normalized=True, mapping=None)[source]#

Returns mixing matrix for attribute.

Parameters:

Ggraph: NetworkX graph object.
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).
nodes: list or iterable (optional): Build the matrix using only nodes in container. The default is all nodes.
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.
normalizedbool (default=True): Return counts if False or probabilities if True.
mappingdictionary, optional: Mapping from node degree to integer index in matrix. If not specified, an arbitrary ordering will be used.

Returns:

m: numpy array: Counts, or joint probability, of occurrence of node degree.

Notes

Definitions of degree mixing matrix vary on whether the matrix should include rows for degree 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. See examples.

Examples

>>> G = nx.star_graph(3)
>>> mix_mat = nx.degree_mixing_matrix(G)
>>> mix_mat
array([[0. , 0.5],
       [0.5, 0. ]])

If you want every possible degree to appear as a row, even if no nodes have that degree, use mapping as follows,

>>> max_degree = max(deg for n, deg in G.degree)
>>> mapping = {x: x for x in range(max_degree + 1)}  # identity mapping
>>> mix_mat = nx.degree_mixing_matrix(G, mapping=mapping)
>>> mix_mat
array([[0. , 0. , 0. , 0. ],
       [0. , 0. , 0. , 0.5],
       [0. , 0. , 0. , 0. ],
       [0. , 0.5, 0. , 0. ]])