+ jXJRt^RIt.ROt]P!RR7RRl4t]P!RR7RRl4t]P!RR7RRl4t]P!RR7RRRRR R /R l4t]PR 4t ]PRR l4t R#)z Eigenvalue spectrum of graphs. Nweight) edge_attrsc^RIpVPP\P!WR7P 44#)a8Returns 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.]) Nr)scipylinalgeigvalshnxlaplacian_matrixtodenseGrsps&& Y/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/linalg/spectrum.pylaplacian_spectrumrs1N 99  b11!CKKM NNc^RIpVPP\P!WR7P 44#)aReturn 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 Nr)rrrr normalized_laplacian_matrixr r s&& rnormalized_laplacian_spectrumr=s56 99   &&q8@@B rc^RIpVPP\P!WR7P 44#)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 Nr)rreigvalsr adjacency_matrixr r s&& radjacency_spectrumr_s06 99  R00BJJL MMrqg? normalizedFc^RIp\P!WW#R7pVPP VP 4RR7#)aAReturns eigenvalues of the magnetic laplacian matrix with phase `q`. Parameters ---------- G : DiGraph Directed graph q : float (default=0.25) The phase of the magnetic potential is the charge parameter 0 <= q <= 0.5. At q=0 returns the standard Laplacian. 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. normalized : bool, optional (default=False) If True, return the spectrum of the normalized magnetic laplacian matrix. If False, use the magnetic laplacian matrix without normalization. Returns ------- evals : np.ndarray Eigenvalues of the magnetic Laplacian matrix Raises ------ NetworkXNotImplemented If `G` is undirected or a multigraph. See Also -------- magnetic_laplacian_matrix N)rrrT) eigvals_only)rr magnetic_laplacian_matrixreightoarray)r rrrrMLs&$$$ rmagnetic_spectrumr!s7F % %aV SB 99>>"**,T> ::rc^RIpVP4'd0VPP\P !V44#VPP\P !V44#)ajReturns 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. N)r is_directedrrr directed_modularity_matrixmodularity_matrix)r rs& rmodularity_spectrumr&sR.}}yy  !>!>q!ABByy  !5!5a!899rc^RIpVPP\P!W4P 44#)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. N)rrrr bethe_hessian_matrixr )r rrs&& rbethe_hessian_spectrumr*s06 99  b55a;CCE FFr)rrr&rr*r!r)N) __doc__networkxr __all__ _dispatchablerrrr!r&r*rrr0s X&(O'(OVX&'BX&N'N>X&%;d%;8%;%;'%;P::<GGr