# networkx.linalg.modularitymatrix.modularity_matrix¶

modularity_matrix(G, nodelist=None, weight=None)[source]

Return the modularity matrix of G.

The modularity matrix is the matrix B = A - <A>, where A is the adjacency matrix and <A> 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

$A_{ij} - {k_i k_j m \over 2}$

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. B – The modularity matrix of G. Numpy matrix

Examples

>>> import networkx as nx
>>> k =[3, 2, 2, 1, 0]
>>> G = nx.havel_hakimi_graph(k)
>>> B = nx.modularity_matrix(G)


to_numpy_matrix(), adjacency_matrix(), laplacian_matrix(), directed_modularity_matrix()