Source code for networkx.algorithms.assortativity.correlation

# -*- coding: utf-8 -*-
"""Node assortativity coefficients and correlation measures.
"""
import networkx as nx
from networkx.algorithms.assortativity.mixing import degree_mixing_matrix, \
    attribute_mixing_matrix, numeric_mixing_matrix
from networkx.algorithms.assortativity.pairs import node_degree_xy, \
    node_attribute_xy
__author__ = ' '.join(['Aric Hagberg <aric.hagberg@gmail.com>',
                       'Oleguer Sagarra <oleguer.sagarra@gmail.com>'])
__all__ = ['degree_pearson_correlation_coefficient',
           'degree_assortativity_coefficient',
           'attribute_assortativity_coefficient',
           'numeric_assortativity_coefficient']


[docs]def 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. Examples -------- >>> G=nx.path_graph(4) >>> r=nx.degree_assortativity_coefficient(G) >>> print("%3.1f"%r) -0.5 See Also -------- attribute_assortativity_coefficient numeric_assortativity_coefficient neighbor_connectivity 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). """ M = degree_mixing_matrix(G, x=x, y=y, nodes=nodes, weight=weight) return numeric_ac(M)
[docs]def degree_pearson_correlation_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. This is the same as degree_assortativity_coefficient but uses the potentially faster scipy.stats.pearsonr function. 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 pearson correlation of degrees only for specified nodes. The default is all nodes. Returns ------- r : float Assortativity of graph by degree. Examples -------- >>> G=nx.path_graph(4) >>> r=nx.degree_pearson_correlation_coefficient(G) >>> print("%3.1f"%r) -0.5 Notes ----- This calls scipy.stats.pearsonr. 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). """ try: import scipy.stats as stats except ImportError: raise ImportError( "Assortativity requires SciPy: http://scipy.org/ ") xy = node_degree_xy(G, x=x, y=y, nodes=nodes, weight=weight) x, y = zip(*xy) return stats.pearsonr(x, y)[0]
[docs]def 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 ---------- G : NetworkX graph attribute : string 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 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 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 """ M = attribute_mixing_matrix(G, attribute, nodes) return attribute_ac(M)
[docs]def numeric_assortativity_coefficient(G, attribute, nodes=None): """Compute assortativity for numerical node attributes. Assortativity measures the similarity of connections in the graph with respect to the given numeric attribute. The numeric attribute must be an integer. Parameters ---------- G : NetworkX graph attribute : string Node attribute key. The corresponding attribute value must be an integer. nodes: list or iterable (optional) Compute numeric assortativity only for attributes of nodes in container. The default is all nodes. Returns ------- r: float Assortativity of graph for given attribute Examples -------- >>> G=nx.Graph() >>> G.add_nodes_from([0,1],size=2) >>> G.add_nodes_from([2,3],size=3) >>> G.add_edges_from([(0,1),(2,3)]) >>> print(nx.numeric_assortativity_coefficient(G,'size')) 1.0 Notes ----- This computes Eq. (21) in Ref. [1]_ , for the mixing matrix of of the specified attribute. References ---------- .. [1] M. E. J. Newman, Mixing patterns in networks Physical Review E, 67 026126, 2003 """ a = numeric_mixing_matrix(G, attribute, nodes) return numeric_ac(a)
def attribute_ac(M): """Compute assortativity for attribute matrix M. Parameters ---------- M : numpy array or matrix Attribute mixing matrix. Notes ----- This computes Eq. (2) in Ref. [1]_ , (trace(e)-sum(e^2))/(1-sum(e^2)), where e 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 """ try: import numpy except ImportError: raise ImportError( "attribute_assortativity requires NumPy: http://scipy.org/ ") if M.sum() != 1.0: M = M / float(M.sum()) M = numpy.asmatrix(M) s = (M * M).sum() t = M.trace() r = (t - s) / (1 - s) return float(r) def numeric_ac(M): # M is a numpy matrix or array # numeric assortativity coefficient, pearsonr try: import numpy except ImportError: raise ImportError('numeric_assortativity requires ', 'NumPy: http://scipy.org/') if M.sum() != 1.0: M = M / float(M.sum()) nx, ny = M.shape # nx=ny x = numpy.arange(nx) y = numpy.arange(ny) a = M.sum(axis=0) b = M.sum(axis=1) vara = (a * x**2).sum() - ((a * x).sum())**2 varb = (b * x**2).sum() - ((b * x).sum())**2 xy = numpy.outer(x, y) ab = numpy.outer(a, b) return (xy * (M - ab)).sum() / numpy.sqrt(vara * varb) # fixture for pytest def setup_module(module): import pytest numpy = pytest.importorskip('numpy') scipy = pytest.importorskip('scipy')