Source code for networkx.linalg.spectrum

"""
Eigenvalue spectrum of graphs.
"""
#    Copyright (C) 2004-2018 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
import networkx as nx
__author__ = "\n".join(['Aric Hagberg <aric.hagberg@gmail.com>',
                        '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']


[docs]def laplacian_spectrum(G, weight='weight'): """Return 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())
[docs]def adjacency_spectrum(G, weight='weight'): """Return 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())
[docs]def modularity_spectrum(G): """Return 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))
# fixture for nose tests def setup_module(module): from nose import SkipTest try: import scipy.linalg except: raise SkipTest("scipy.linalg not available")