a «J5d$ã@sHdZddlZgd¢Zddd„Zddd„Zdd d „Zd d „Zdd d„ZdS)z Eigenvalue spectrum of graphs. éN)Úlaplacian_spectrumÚadjacency_spectrumÚmodularity_spectrumÚnormalized_laplacian_spectrumÚbethe_hessian_spectrumÚweightcCs*ddl}ddl}|j tj||d ¡¡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 to_numpy_array for other options. See Also -------- laplacian_matrix rN©r)ÚscipyÚ scipy.linalgÚlinalgÚeigvalshÚnxZlaplacian_matrixÚtodense©ÚGrÚspr ©rúT/var/www/html/django/DPS/env/lib/python3.9/site-packages/networkx/linalg/spectrum.pyrsrcCs*ddl}ddl}|j tj||d ¡¡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 r r Znormalized_laplacian_matrixrrrrrr/s ÿrcCs*ddl}ddl}|j tj||d ¡¡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 Úeigvalsr Zadjacency_matrixrrrrrrQsrcCs@ddl}ddl}| ¡r*|j t |¡¡S|j t |¡¡SdS)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 rr Zdirected_modularity_matrixZmodularity_matrix)rrr rrrrqs 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 r Zbethe_hessian_matrixr)rÚrrr rrrrsr)r)r)r)N) Ú__doc__Znetworkxr Ú__all__rrrrrrrrrÚs "