o ˷e$@sHdZddlZgdZdddZdddZdd d Zd d Zdd dZdS)z Eigenvalue spectrum of graphs. N)laplacian_spectrumadjacency_spectrummodularity_spectrumnormalized_laplacian_spectrumbethe_hessian_spectrumweightcC*ddl}ddl}|jtj||dS)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 rNr)scipy scipy.linalglinalgeigvalshnxlaplacian_matrixtodenseGrspr rO/var/www/ideatree/venv/lib/python3.10/site-packages/networkx/linalg/spectrum.pyrrcCr)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 rnormalized_laplacian_matrixrrrrrr/s rcCr)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_matrixrrrrrrQrrcCs<ddl}ddl}|r|jt|S|jt|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 rrrrqs rcCs(ddl}ddl}|jt||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 r rbethe_hessian_matrixr)rrrr rrrrsrr )N) __doc__networkxr__all__rrrrrrrrrs "