## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/assortativity/correlation.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |

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"""Node assortativity coefficients and correlation measures. """ from networkx.algorithms.assortativity.mixing import ( degree_mixing_matrix, attribute_mixing_matrix, numeric_mixing_matrix, ) from networkx.algorithms.assortativity.pairs import node_degree_xy __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(f"{r:3.1f}") -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) >>> print(f"{r:3.1f}") -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 as e: raise ImportError("Assortativity requires SciPy:" "http://scipy.org/ ") from e 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^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) 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.ndarray 2D ndarray representing the 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 as e: raise ImportError( "attribute_assortativity requires " "NumPy: http://scipy.org/" ) from e if M.sum() != 1.0: M = M / M.sum() s = (M @ M).sum() t = M.trace() r = (t - s) / (1 - s) return r def numeric_ac(M): # M is a numpy matrix or array # numeric assortativity coefficient, pearsonr try: import numpy except ImportError as e: raise ImportError( "numeric_assortativity requires " "NumPy: http://scipy.org/" ) from e 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)