def test_bethe_hessian(self):
"Bethe Hessian matrix"
# fmt: off
H = np.array([[4, -2, 0], [-2, 5, -2], [0, -2, 4]])
# fmt: on
permutation = [2, 0, 1]
# Bethe Hessian gives expected form
np.testing.assert_equal(
nx.bethe_hessian_matrix(self.P, r=2).todense(), H)
# nodelist is correctly implemented
np.testing.assert_equal(
nx.bethe_hessian_matrix(self.P, r=2,
nodelist=permutation).todense(),
H[np.ix_(permutation, permutation)],
)
# Equal to Laplacian matrix when r=1
np.testing.assert_equal(
nx.bethe_hessian_matrix(self.G, r=1).todense(),
nx.laplacian_matrix(self.G).todense(),
)
# Correct default for the regularizer r
np.testing.assert_equal(
nx.bethe_hessian_matrix(self.G).todense(),
nx.bethe_hessian_matrix(self.G, r=1.25).todense(),
)
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())
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())
def test_bethe_hessian(self):
"Bethe Hessian matrix"
H = numpy.array([[ 4, -2, 0],
[-2, 5, -2],
[ 0, -2, 4]])
permutation = [2, 0, 1]
# Bethe Hessian gives expected form
assert_equal(nx.bethe_hessian_matrix(self.P, r=2).todense(), H)
# nodelist is correctly implemented
assert_equal(nx.bethe_hessian_matrix(self.P, r=2, nodelist=permutation).todense(),
H[numpy.ix_(permutation, permutation)])
# Equal to Laplacian matrix when r=1
assert_equal(nx.bethe_hessian_matrix(self.G, r=1).todense(),
nx.laplacian_matrix(self.G).todense())
# Correct default for the regularizer r
assert_equal(nx.bethe_hessian_matrix(self.G).todense(),
nx.bethe_hessian_matrix(self.G, r=1.25).todense())