pedWorks.py 文件源码

def directed_modularity_matrix(G, nodelist=None):
    """ INCLUDED FOR TESTING PURPOSES - Not implemented yet.

    Return the directed modularity matrix of G.
    The modularity matrix is the matrix B = A - <A>, where A is the adjacency
    matrix and <A> 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
        B_ij = A_ij - k_i(out) k_j(in)/m
    where k_i(in) is the in degree of node i, and k_j(out) is the out degree
    of node j, with m the number of edges in the graph.
    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().
    Returns
    -------
    B : Numpy matrix
      The modularity matrix of 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.
    """
    if nodelist is None:
        nodelist = G.nodes()
    A = nx.to_scipy_sparse_matrix(G, nodelist=nodelist, format='csr')
    k_in = A.sum(axis=0)
    k_out = A.sum(axis=1)
    m = G.number_of_edges()
    # Expected adjacency matrix
    X = k_out * k_in / m
    return A - X