def modularity_mx()

in src/qubo_community.py [0:0]

• 10 lines of code
• 5 McCabe index (conditional complexity)

def modularity_mx(nx_G):
    """
    Create a sparse matrix for the modularity of a graph nx_G

    :param nx_G: networkX graph
    :return: scipy coo sparse matrix, the modularity matrix for nx_G with weighted edges
    """
    
    # Generate a sparse adjacency matrix using networkx
    adj = nx.adjacency_matrix(nx_G, nodelist=sorted(list(nx_G)), weight='weight')
    
    # Create a numpy array for node's degree. 
    # Here we assumed an undirected graph, so `degrees` refers to both the in-degree and out-degree
    sorted_degrees = sorted(nx_G.degree(weight='weight'))
    degrees = np.array([degree[1] for degree in sorted_degrees])
    m = sum(degrees) / 2

    # Calculate the expected number of edges between two nodes for a null model.
    # Note we use sparse matrix format here but this degree matrix is a dense one by definition
    degrees = np.expand_dims(degrees.squeeze(), axis=0)
    degree_mx = sp.csr_matrix(degrees.T).multiply(sp.csr_matrix(degrees)) / (2 * m)
    
    # Create a modularity matrix and convert it into coo sparse matrix format (Torch sparse tensor compatible)
    modu_mx_sparse = (sp.csr_matrix(adj) - degree_mx) / (2 * m)
    modu_mx_sparse = sp.coo_matrix(modu_mx_sparse)

    return modu_mx_sparse