def vnge_naive(adjacency):
"""Computes Von Neumann Graph Entropy (VNGE) with full eigendecomposition.
Args:
adjacency (spmatrix): Input sparse adjacency matrix of a graph.
Returns:
float: Von Neumann entropy of the graph.
"""
density = laplacian(adjacency, normalized=False)
density.data /= np.sum(density.diagonal())
eigenvalues, _ = scipy.linalg.eigh(density.todense())
return -np.where(eigenvalues > 0, eigenvalues * np.log(eigenvalues),
0).sum()
def netlsd_naive(adjacency, timescales=np.logspace(-2, 2, 256)):
"""Computes NetLSD with full eigendecomposition, in a naïve way.
Args:
adjacency (spmatrix): Input sparse adjacency matrix of a graph.
timescales (np.ndarray): A 1D array with the timescale parameter of NetLSD.
Default value is the one used in both NetLSD and SLaQ papers.
Returns:
np.ndarray: NetLSD descriptors of the graph.
"""
lap = laplacian(adjacency)
lambdas, _ = scipy.linalg.eigh(lap.todense())
return np.exp(-np.outer(timescales, lambdas)).sum(axis=-1)
def vnge(adjacency, lanczos_steps=10, nvectors=100):
"""Computes Von Neumann Graph Entropy (VNGE) using SLaQ.
Args:
adjacency (scipy.sparse.base.spmatrix): Input adjacency matrix of a graph.
lanczos_steps (int): Number of Lanczos steps. Setting lanczos_steps=10 is
the default from SLaQ.
nvectors (int): Number of random vectors for stochastic estimation. Setting
nvectors=10 is the default values from the SLaQ paper.
Returns:
float: Approximated VNGE.
"""
if adjacency.nnz == 0: # By convention, if x=0, x*log(x)=0.
return 0
density = laplacian(adjacency, False)
density.data /= np.sum(density.diagonal()).astype(np.float32)
return _slq_red_var_vnge(density, lanczos_steps, nvectors)
def netlsd(adjacency,
timescales=np.logspace(-2, 2, 256),
lanczos_steps=10,
nvectors=100,
normalization=None):
"""Computes NetLSD descriptors using SLaQ.
Args:
adjacency (sparse matrix): Input adjacency matrix of a graph.
timescales (np.ndarray): Timescale parameter for NetLSD computation. Default
value is the one used in both NetLSD and SLaQ papers.
lanczos_steps (int): Number of Lanczos steps. Setting lanczos_steps=10 is
the default from SLaQ.
nvectors (int): Number of random vectors for stochastic estimation. Setting
nvectors=10 is the default values from the SLaQ paper.
normalization (str): Normalization type for NetLSD.
Returns:
np.ndarray: Approximated NetLSD descriptors.
"""
lap = laplacian(adjacency, True)
hkt = _slq_red_var_netlsd(
lap, lanczos_steps, nvectors,
timescales) # Approximated Heat Kernel Trace (hkt).
if normalization is None:
return hkt
n = lap.shape[0]
if normalization == 'empty':
return hkt / n
elif normalization == 'complete':
return hkt / (1 + (n - 1) * np.exp(-timescales))
elif normalization is None:
return hkt
else:
raise ValueError(
"Unknown normalization type: expected one of [None, 'empty', 'complete'], got",
normalization)