| #-*- 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'] |
| |
| 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) |
| |
| |
| 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) |
| >>> 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] |
| |
| |
| 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))/(1-sum(M), |
| 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) |
| |
| |
| 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. |
| |
| Parameters |
| ---------- |
| G : NetworkX graph |
| |
| attribute : string |
| Node attribute key |
| |
| 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))/(1-sum(e)), |
| 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 nose tests |
| def setup_module(module): |
| from nose import SkipTest |
| try: |
| import numpy |
| except: |
| raise SkipTest("NumPy not available") |
| try: |
| import scipy |
| except: |
| raise SkipTest("SciPy not available") |
