B ,[?@s~dZddlmZddlZddlmZddddd gZd d gZ ed ed ddd Z eded ddd Z ddZ dS)zModularity matrix of graphs. )divisionN)not_implemented_for z%Aric Hagberg zPieter Swart (swart@lanl.gov)z Dan Schult (dschult@colgate.edu)z1Jean-Gabriel Young (Jean.gabriel.young@gmail.com)modularity_matrixdirected_modularity_matrixZdirectedZ multigraphcCsV|dkrt|}tj|||dd}|jdd}|d}||d|}||S)aReturn the modularity matrix of G. The modularity matrix is the matrix B = A - , where A is the adjacency matrix and is the average adjacency matrix, assuming that the graph is described by the configuration model. More specifically, the element B_ij of B is defined as .. math:: A_{ij} - {k_i k_j m \over 2} where k_i is the degree of node i, and were m is the number of edges in the graph. When weight is set to a name of an attribute edge, Aij, k_i, k_j and m are computed using its value. Parameters ---------- G : Graph A NetworkX graph nodelist : list, optional The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). weight : string or None, optional (default=None) The edge attribute that holds the numerical value used for the edge weight. If None then all edge weights are 1. Returns ------- B : Numpy matrix The modularity matrix of G. Examples -------- >>> import networkx as nx >>> k =[3, 2, 2, 1, 0] >>> G = nx.havel_hakimi_graph(k) >>> B = nx.modularity_matrix(G) See Also -------- to_numpy_matrix adjacency_matrix laplacian_matrix directed_modularity_matrix References ---------- .. [1] M. E. J. Newman, "Modularity and community structure in networks", Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006. Ncsr)nodelistweightformat)axisg?)listnxto_scipy_sparse_matrixsumZ transpose)Grr AkmXr?lib/python3.7/site-packages/networkx/linalg/modularitymatrix.pyrs8   Z undirectedcCsV|dkrt|}tj|||dd}|jdd}|jdd}|}|||}||S)aReturn the directed modularity matrix of G. The modularity matrix is the matrix B = A - , where A is the adjacency matrix and is the expected adjacency matrix, assuming that the graph is described by the configuration model. More specifically, the element B_ij of B is defined as .. math:: B_{ij} = A_{ij} - k_i^{out} k_j^{in} / m where :math:`k_i^{in}` is the in degree of node i, and :math:`k_j^{out}` is the out degree of node j, with m the number of edges in the graph. When weight is set to a name of an attribute edge, Aij, k_i, k_j and m are computed using its value. Parameters ---------- G : DiGraph A NetworkX DiGraph nodelist : list, optional The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). weight : string or None, optional (default=None) The edge attribute that holds the numerical value used for the edge weight. If None then all edge weights are 1. Returns ------- B : Numpy matrix The modularity matrix of G. Examples -------- >>> import networkx as nx >>> G = nx.DiGraph() >>> G.add_edges_from(((1,2), (1,3), (3,1), (3,2), (3,5), (4,5), (4,6), ... (5,4), (5,6), (6,4))) >>> B = nx.directed_modularity_matrix(G) Notes ----- NetworkX defines the element A_ij of the adjacency matrix as 1 if there is a link going from node i to node j. Leicht and Newman use the opposite definition. This explains the different expression for B_ij. See Also -------- to_numpy_matrix adjacency_matrix laplacian_matrix modularity_matrix References ---------- .. [1] E. A. Leicht, M. E. J. Newman, "Community structure in directed networks", Phys. Rev Lett., vol. 100, no. 11, p. 118703, 2008. Nr)rr r r)r r )rrrr)rrr rZk_inZk_outrrrrrrVsA    cCs:ddlm}yddl}ddl}Wn|dYnXdS)Nr)SkipTestzNumPy not available)Znosernumpyscipy)modulerrrrrr setup_modules   r)NN)NN) __doc__Z __future__rZnetworkxrZnetworkx.utilsrjoin __author____all__rrrrrrrs  AL