o 9e¾ã@sHdZddlZgd¢Zddd„Zddd„Zdd d „Zd d „Zdd d„ZdS)z Eigenvalue spectrum of graphs. éN)Úlaplacian_spectrumÚadjacency_spectrumÚmodularity_spectrumÚnormalized_laplacian_spectrumÚbethe_hessian_spectrumÚweightcCó*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 ©rúHD:\Projects\ConvertPro\env\Lib\site-packages\networkx/linalg/spectrum.pyrs&rcCr)a#Return eigenvalues of the normalized 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 to_numpy_array for other options. See Also -------- normalized_laplacian_matrix rNr )r r r r rZnormalized_laplacian_matrixrrrrrr;s ÿrcCr)aReturns eigenvalues of the adjacency matrix 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 to_numpy_array for other options. See Also -------- adjacency_matrix rNr )r r r ÚeigvalsrZadjacency_matrixrrrrrr]srcCs<ddl}ddl}| ¡r|j t |¡¡S|j t |¡¡S)aªReturns eigenvalues of the modularity matrix of G. Parameters ---------- G : Graph A NetworkX Graph or DiGraph Returns ------- evals : NumPy array Eigenvalues See Also -------- 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. rN)r r Z is_directedr rrZdirected_modularity_matrixZmodularity_matrix)rrr rrrr}s rcCs(ddl}ddl}|j t ||¡ ¡¡S)uþReturns eigenvalues of the Bethe Hessian matrix of G. Parameters ---------- G : Graph A NetworkX Graph or DiGraph r : float Regularizer parameter Returns ------- evals : NumPy array Eigenvalues See Also -------- bethe_hessian_matrix References ---------- .. [1] A. Saade, F. Krzakala and L. Zdeborová "Spectral clustering of graphs with the bethe hessian", Advances in Neural Information Processing Systems. 2014. rN)r r r r rZbethe_hessian_matrixr)rÚrrr rrrrœsrr )N) Ú__doc__ZnetworkxrÚ__all__rrrrrrrrrÚs , "