Gd@dZddlZgdZd dZd dZd dZdZd d ZdS) z Eigenvalue spectrum of graphs. N)laplacian_spectrumadjacency_spectrummodularity_spectrumnormalized_laplacian_spectrumbethe_hessian_spectrumweightcddl}ddl}|jt j||S)aReturns 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.]) rNr)scipy scipy.linalglinalgeigvalshnxlaplacian_matrixtodenseGrspr s 8lib/python3.11/site-packages/networkx/linalg/spectrum.pyrrsOL 9  b1!FCCCKKMM N NNcddl}ddl}|jt j||S)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 rrnormalized_laplacian_matrixrrs rrr;sU4 9   &q888@@BB  rcddl}ddl}|jt j||S)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 eigvalsradjacency_matrixrrs rrr]sN4 9  R06BBBJJLL M MMrcddl}ddl}|r,|jt j|S|jt j|S)aReturns 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 is_directedr rrdirected_modularity_matrixmodularity_matrix)rrr s rrr}sn,}}:y  !>q!A!ABBBy  !5a!8!8999rcddl}ddl}|jt j||S)uReturns 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 rrbethe_hessian_matrixr)rrrr s rrrsK4 9  b5a;;CCEE F FFrr )N) __doc__networkxr__all__rrrrrrrr's   )O)O)O)OXDNNNN@:::>GGGGGGr