forked from 170010011/fr
167 lines
3.6 KiB
Python
167 lines
3.6 KiB
Python
"""
|
|
Eigenvalue spectrum of graphs.
|
|
"""
|
|
import networkx as nx
|
|
|
|
__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_array 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_array 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_array 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())
|