networkx.linalg.modularity_matrix¶

networkx.linalg.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 / 2 * m

where k_i(in) 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.

See also

to_numpy_matrix, adjacency_matrix, laplacian_matrix, directed_modularity_matrix

References

[R1182]

M. E. J. Newman, “Modularity and community structure in networks”, Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.

Examples

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