ó ú£Õ\c@sÌdZddlZddlmZmZmZddlmZm Z dj ddgƒZ dd d d gZ d d ddd„Zd d ddd„Zdd„Zdd„Zd„Zd„Zd„ZdS(s:Node assortativity coefficients and correlation measures. iÿÿÿÿN(tdegree_mixing_matrixtattribute_mixing_matrixtnumeric_mixing_matrix(tnode_degree_xytnode_attribute_xyt s%Aric Hagberg s+Oleguer Sagarra t&degree_pearson_correlation_coefficientt degree_assortativity_coefficientt#attribute_assortativity_coefficientt!numeric_assortativity_coefficienttouttinc Cs.t|d|d|d|d|ƒ}t|ƒS(sÇCompute 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). txtytnodestweight(Rt numeric_ac(tGR R RRtM((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyRs<$c Cs}yddlj}Wntk r2tdƒ‚nXt|d|d|d|d|ƒ}t|Œ\}}|j||ƒdS( s·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). iÿÿÿÿNs0Assortativity requires SciPy: http://scipy.org/ R R RRi(t scipy.statststatst ImportErrorRtziptpearsonr(RR R RRRtxy((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyRPs4  $cCst|||ƒ}t|ƒS(s-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 (Rt attribute_ac(Rt attributeRR((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyRŽs*cCst|||ƒ}t|ƒS(sCompute 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 (RR(RRRta((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyR ¼s)cCs¢yddl}Wntk r/tdƒ‚nX|jƒdkr[|t|jƒƒ}n|j|ƒ}||jƒ}|jƒ}||d|}t|ƒS(sÐCompute 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 iÿÿÿÿNs:attribute_assortativity requires NumPy: http://scipy.org/ gð?i(tnumpyRtsumtfloattasmatrixttrace(RRtstttr((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyRés   c CsByddl}Wn tk r2tddƒ‚nX|jƒdkr^|t|jƒƒ}n|j\}}|j|ƒ}|j|ƒ}|jddƒ}|jddƒ}||djƒ||jƒd}||djƒ||jƒd} |j||ƒ} |j||ƒ} | || jƒ|j|| ƒS( Niÿÿÿÿsnumeric_assortativity requires sNumPy: http://scipy.org/gð?taxisiii(RRRRtshapetarangetoutertsqrt( RRtnxtnyR R RtbtvaratvarbRtab((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyR s"  &&cCs`ddlm}yddl}Wn|dƒ‚nXyddl}Wn|dƒ‚nXdS(Niÿÿÿÿ(tSkipTestsNumPy not availablesSciPy not available(tnoseR/Rtscipy(tmoduleR/RR1((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyt setup_module!s(t__doc__tnetworkxR)t(networkx.algorithms.assortativity.mixingRRRt'networkx.algorithms.assortativity.pairsRRtjoint __author__t__all__tNoneRRRR RRR3(((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/assortativity/correlation.pyts$      ?= . - !