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## iof-tools / networkxMiCe / networkx-master / networkx / linalg / spectrum.py @ 5cef0f13

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 1 ```""" ``` ```Eigenvalue spectrum of graphs. ``` ```""" ``` ```# Copyright (C) 2004-2019 by ``` ```# Aric Hagberg ``` ```# Dan Schult ``` ```# Pieter Swart ``` ```# All rights reserved. ``` ```# BSD license. ``` ```import networkx as nx ``` ```__author__ = "\n".join(['Aric Hagberg ', ``` ``` 'Pieter Swart (swart@lanl.gov)', ``` ``` 'Dan Schult(dschult@colgate.edu)', ``` ``` 'Jean-Gabriel Young (jean.gabriel.young@gmail.com)']) ``` ```__all__ = ['laplacian_spectrum', 'adjacency_spectrum', 'modularity_spectrum', ``` ``` 'normalized_laplacian_spectrum', 'bethe_hessian_spectrum'] ``` ```def laplacian_spectrum(G, weight='weight'): ``` ``` """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 to_numpy_matrix for other options. ``` ``` ``` ``` See Also ``` ``` -------- ``` ``` laplacian_matrix ``` ``` """ ``` ``` from scipy.linalg import eigvalsh ``` ``` return eigvalsh(nx.laplacian_matrix(G, weight=weight).todense()) ``` ```def normalized_laplacian_spectrum(G, weight='weight'): ``` ``` """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_matrix for other options. ``` ``` ``` ``` See Also ``` ``` -------- ``` ``` normalized_laplacian_matrix ``` ``` """ ``` ``` from scipy.linalg import eigvalsh ``` ``` return eigvalsh(nx.normalized_laplacian_matrix(G, weight=weight).todense()) ``` ```def adjacency_spectrum(G, weight='weight'): ``` ``` """Returns 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_matrix for other options. ``` ``` ``` ``` See Also ``` ``` -------- ``` ``` adjacency_matrix ``` ``` """ ``` ``` from scipy.linalg import eigvals ``` ``` return eigvals(nx.adjacency_matrix(G, weight=weight).todense()) ``` ```def modularity_spectrum(G): ``` ``` """Returns 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. ``` ``` """ ``` ``` from scipy.linalg import eigvals ``` ``` if G.is_directed(): ``` ``` return eigvals(nx.directed_modularity_matrix(G)) ``` ``` else: ``` ``` return eigvals(nx.modularity_matrix(G)) ``` ```def bethe_hessian_spectrum(G, r=None): ``` ``` """Returns 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. ``` ``` """ ``` ``` from scipy.linalg import eigvalsh ``` ``` return eigvalsh(nx.bethe_hessian_matrix(G, r).todense()) ``` ``` ``` ```# fixture for nose tests ``` ```def setup_module(module): ``` ``` from nose import SkipTest ``` ``` try: ``` ``` import scipy.linalg ``` ``` except: ``` ``` raise SkipTest("scipy.linalg not available") ```