Source code for networkx.linalg.spectrum

"""
Eigenvalue spectrum of graphs.
"""
import networkx as nx

__all__ = [
    "laplacian_spectrum",
    "adjacency_spectrum",
    "modularity_spectrum",
    "normalized_laplacian_spectrum",
    "bethe_hessian_spectrum",
]


[docs] @nx._dispatchable(edge_attrs="weight") 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 :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.]) """ import scipy as sp return sp.linalg.eigvalsh(nx.laplacian_matrix(G, weight=weight).todense())
[docs] @nx._dispatchable(edge_attrs="weight") 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_array for other options. See Also -------- normalized_laplacian_matrix """ import scipy as sp return sp.linalg.eigvalsh( nx.normalized_laplacian_matrix(G, weight=weight).todense() )
[docs] @nx._dispatchable(edge_attrs="weight") 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_array for other options. See Also -------- adjacency_matrix """ import scipy as sp return sp.linalg.eigvals(nx.adjacency_matrix(G, weight=weight).todense())
[docs] @nx._dispatchable 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. """ import scipy as sp if G.is_directed(): return sp.linalg.eigvals(nx.directed_modularity_matrix(G)) else: return sp.linalg.eigvals(nx.modularity_matrix(G))
[docs] @nx._dispatchable 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. Zdeborov√° "Spectral clustering of graphs with the bethe hessian", Advances in Neural Information Processing Systems. 2014. """ import scipy as sp return sp.linalg.eigvalsh(nx.bethe_hessian_matrix(G, r).todense())