U 9v f¾ã@sNdZddlZdddddgZdd d„Zdd d„Zdd d„Zd d„Zdd d„ZdS)z Eigenvalue spectrum of graphs. éNÚlaplacian_spectrumÚadjacency_spectrumÚmodularity_spectrumÚnormalized_laplacian_spectrumÚbethe_hessian_spectrumÚweightcCs*ddl}ddl}|j tj||d ¡¡S)a¨Returns eigenvalues of the Laplacian of G Parameters ---------- G : graph A NetworkX graph weight : string or None, optional (default='weight') The edge data key used to compute each value in the matrix. If None, then each edge has weight 1. Returns ------- evals : NumPy array Eigenvalues Notes ----- For MultiGraph/MultiDiGraph, the edges weights are summed. See :func:`~networkx.convert_matrix.to_numpy_array` for other options. See Also -------- laplacian_matrix Examples -------- The multiplicity of 0 as an eigenvalue of the laplacian matrix is equal to the number of connected components of G. >>> G = nx.Graph() # Create a graph with 5 nodes and 3 connected components >>> G.add_nodes_from(range(5)) >>> G.add_edges_from([(0, 2), (3, 4)]) >>> nx.laplacian_spectrum(G) array([0., 0., 0., 2., 2.]) rN©r)ÚscipyÚ scipy.linalgÚlinalgÚeigvalshÚnxZlaplacian_matrixÚtodense©ÚGrÚspr ©rúsû , "