view env/lib/python3.9/site-packages/networkx/linalg/spectrum.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
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"""
Eigenvalue spectrum of graphs.
"""
import networkx as nx

__all__ = [
"laplacian_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.

--------
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.

--------
normalized_laplacian_matrix
"""
from scipy.linalg import eigvalsh

return eigvalsh(nx.normalized_laplacian_matrix(G, weight=weight).todense())

"""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.

--------
"""
from scipy.linalg import eigvals

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

--------
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