modularity_matrix#
- modularity_matrix(G, nodelist=None, weight=None)[source]#
Returns 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
\[A_{ij} - {k_i k_j \over 2 m}\]where k_i is the degree of node i, and where 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:
- GGraph
A NetworkX graph
- nodelistlist, 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().
- weightstring 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:
- BNumpy matrix
The modularity matrix of G.
See also
to_numpy_array
modularity_spectrum
adjacency_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.
Examples
>>> k = [3, 2, 2, 1, 0] >>> G = nx.havel_hakimi_graph(k) >>> B = nx.modularity_matrix(G)