def test_to_graph_tool(self):
from graph_tool.spectral import adjacency
for G in self.graphs + [self.weighted]:
gt = G.to_graph_tool()
if G.is_weighted():
adj = adjacency(gt, weight=gt.ep['weight']).A.T
else:
adj = adjacency(gt).A.T
assert_array_equal(G.matrix('dense'), adj)
def test_to_graph_tool(self):
from graph_tool.spectral import adjacency
for G in self.graphs + [self.weighted]:
gt = G.to_graph_tool()
if G.is_weighted():
adj = adjacency(gt, weight=gt.ep['weight']).A.T
else:
adj = adjacency(gt).A.T
assert_array_equal(G.matrix(dense=True), adj)
def cycle_signature(inGraph, maxCycleLength, mode="transition", normalize=True):
assert(mode == "transition" or mode == "adjacency")
if mode == "transition":
A = spectral.transition(inGraph)
if mode == "adjacency":
A = spectral.adjacency(inGraph)
temp = A.copy()
n = A.shape[0] # Number of nodes.
sigs = np.empty((maxCycleLength, n))
if mode == "transition":
for t in xrange(maxCycleLength):
temp = temp.dot(A)
sigs[t,:] = temp.diagonal()
if mode == "adjacency":
for t in xrange(maxCycleLength):
temp = temp.dot(A)
if normalize:
sigs[t,:] = temp.diagonal() / np.sum(temp.diagonal()) # factorial(t+1)
else:
sigs[t,:] = temp.diagonal()
return np.transpose(sigs)
def gt_graph_to_adj_matrix(g: gt.Graph,
edge_weights: Optional[gt.EdgePropertyMap] = NOT_SET,
dtype: str = T.float_x(),
device: Optional[str] = None,
) -> T.SparseTensor:
if edge_weights is NOT_SET:
if 'weights' in g.ep:
edge_weights = g.ep['weights']
else:
edge_weights = None
adj_matrix = spectral.adjacency(g, weight=edge_weights)
return T.sparse.from_spmatrix(
adj_matrix, dtype=dtype, device=device, force_coalesced=True)
def makeISOLaplacians(graphExample, gcc, save=False, saveAt=None):
g = load_GT_graph(
graphExample, gcc, removeSL=True, removePE=True
) #For forming the Laplacian, we have to remove the Self-Loops and Parallel Edges if any.
Ag = spectral.adjacency(g).todense(
) #Despite this todense() the Laplacian is going to be sparse. It is though taking more time to create it.
gp, forwardMap = createIsoGraph(Ag)
Lg = spectral.laplacian(g) #create the Laplacians
Lgp = spectral.laplacian(gp)
if save:
assert (saveAt != None)
save_data(saveAt, Lg, Lgp, forwardMap)
return Lg, Lgp, forwardMap
def makeISOPoisson(numberOfNodes, averDegree, gcc, save=False, saveAt=None):
def degreeSample():
return np.random.poisson(averDegree)
g = generation.random_graph(numberOfNodes, degreeSample, directed=False)
if gcc:
l = topology.label_largest_component(
g) #Keep Largest Connected Component
g.set_vertex_filter(l)
g.purge_vertices()
Ag = spectral.adjacency(g).todense()
gp, forwardMap = graph_analysis.IO.createIsoGraph(Ag)
if save:
assert (saveAt != None)
graph_analysis.IO.save_data(saveAt, g, gp, forwardMap)
return g, gp, forwardMap
def vertex_sim(inGraph, alpha=.95, dist=False):
'''
Implementation of the node similarity metric described in
"Vertex Similarity in networks, Leicht, Holme, Newman."
'''
n = inGraph.num_vertices()
A = spectral.adjacency(inGraph)
evals, evecs = linalg.eigsh(A, k=1, which='LM', tol=1E-3)
scale = alpha / evals[0]
S = linalg.inv(identity(n, format='csc') - scale * A.tocsc())
d = inGraph.degree_property_map("total").a
S = diags(1.0 / d, 0) * S * diags(1.0 / d, 0)
S[np.diag_indices_from(S)] = 1 # Each node is self-similar.
if dist:
S = 1 - S.toarray()
S = 0.5 * (S + S.T
) # Force S to be symmetric and guards to numerical errors.
return S
def __init__(self, graph, k, weight=None):
if k >= graph.num_vertices():
raise ValueError('k must be in the range ' +
'[0, graph.num_vertices()). ' +
'This is due to scipy.sparse.linalg restrictions')
self.lap = gt_spectral.laplacian(graph, normalized=True, weight=weight)
self.adj = gt_spectral.adjacency(graph, weight=weight)
self._deg_vec = np.asarray(self.adj.sum(axis=1))
self._weight = weight
self._vol_graph = utils.graph_volume(graph, self._weight)
self._n = graph.num_vertices()
self._vertex_index = graph.vertex_index
self.eig_val, self.eig_vec = eigsh(self.lap, k, which='SM')
self._deg_vec = np.asarray(self.adj.sum(axis=1))
self.basis = np.multiply(np.power(self._deg_vec, -0.5), self.eig_vec)
self._deg_vec = np.squeeze(self._deg_vec)
def write_motifs_results(output, motifs_list, z_scores,
n_shuf, model="uncorrelated"):
"""Write the adjacency matrix of motifs in the `motifs_list`
and its corresponding z-scores to file.
Naming convention: blogcatalog_3um.motifslog
Parameters
==========
output: name of file will be writen to disk
motifs_list: list of motifs (graph-tool graph instances)
z_scores: corresponding z_scores to each motif.
n_shuf: number of random graph generated
model: name of the random graph generation algorithm"""
assert len(motifs_list) == len(z_scores)
with open(output, 'w') as f:
f.write("Number of shuffles: {} ({})\n".format(n_shuf, model))
for i, m in enumerate(motifs_list):
f.write("Motif {} - z-score: {}\n".format(i+1, z_scores[i]))
for rows in adjacency(m).toarray():
f.write(str(rows) + '\n')
f.write('\n')
return output
def signLessLaplacianSpectrum(inGraph, graphName, eigsToCompute="all", save=True):
'''
Assumes the inGraph is connected.
'''
if eigsToCompute == "all":
eigsToCompute = inGraph.num_vertices() - 1
eigsWhere = "../Data/Spectrums/SignLess_L/"+graphName+"_"+str(eigsToCompute)+"_Eigs"
if os.path.isfile(eigsWhere):
print "Loading Spectrum"
evals, evecs = IO.load_data(eigsWhere)
else:
Ld = spectral.laplacian(inGraph).diagonal() #TODO replace with degree vector to avoid building the laplacian
Ls = spectral.adjacency(inGraph)
Ls.setdiag(Ld)
evals, evecs = computeSpectrum(Ls, eigsToCompute, small=False) #For sign less Laplacian big eigpairs matter
#sort so that big eigen-pairs are first
evals = evals[::-1]
evecs = np.flipud(evecs)
if save:
IO.save_data(eigsWhere, evals, evecs)
return evals, evecs
def panos_sim_4(inGraph,
graphName,
eigs="all",
strategy=None,
compressed=True,
sigma=0.1):
A = spectral.adjacency(inGraph)
degrees = inGraph.degree_property_map("total").a
M = A + diags(degrees + 1, 0)
if eigs == "all":
eigs = len(degrees) - 1
evals, evecs = gk.computeSpectrum(M, eigs, small=False, verbose=True)
print evals
n = evecs.shape[1] # Number of nodes.
signatures = np.empty((n, len(evals)))
squaredEigVectors = evecs**2
squaredEigVectors = np.transpose(evecs)
# for node in xrange(n):
# signatures[node, :] = squaredEigVectors[node, :] * ((degrees[node] - evals)**2)
#
# for i in xrange(10):
# signaturesNew = gk.neighbor_signatures(signatures, inGraph, "average")
# if np.allclose(signatures, signaturesNew):
# break
# signatures = signaturesNew
if compressed:
signatures = compress_spectral_signatures(signatures,
evals,
sigma=sigma)
print "Signature was created."
return signatures
def compute_bounds(g):
"""Computes bounds for chromatic number based on hoffman bound, generalized hoffman bound, woc-elp conjetural bound, and wilf's theorem.
Takes a graph and computes the bounds, then outputs a summary array which includes vertex degree information and an estimate for
the actual chromatic number of the graph based on actual colorings.
Args:
g (graph_tool graph)
Returns:
numpy array [hoffman bound, generalized hoffman bound, woc-elp bound, wilf bound, max degree, average degree, computed coloring number]
"""
# Get degree info
n = g.num_vertices()
m = g.num_edges()
average_degree = 2 * m / n
max_degree = max([vertex.out_degree() for vertex in g.vertices()])
# Get spectral info
A = spectral.adjacency(g)
Aw, Av = linalg.eig(A.todense())
eigenvalues = sorted(Aw, reverse=True)
results = []
# compute eigen-bounds
results.append(compute_hoff(eigenvalues))
results.append(compute_gen_hoff(eigenvalues))
results.append(compute_woc_elp(eigenvalues))
results.append(compute_wilf(eigenvalues))
# stats
results.append(max_degree)
results.append(average_degree)
# compute coloring
results.append(get_best_coloring(g)[0])
return numpy.array(results)
def get_mat_adjacency(self): return adjacency(self.__graph, self.get_weights())
def getAdjacency(self): if self.isWeighted(): return adjacency(self.graph, self.graph.edge_properties["weight"]) else: return adjacency(self.graph)
def adjacency_matrix(graph, weight=None):
return adjacency(graph, weight).toarray().T
def getAdjacency(self):
if self.isWeighted():
return adjacency(self.graph, self.graph.edge_properties["weight"])
else:
return adjacency(self.graph)
from evolution import * import numpy as np from math import inf from time import time import array from optimized.cyFns import * from cpython cimport array from libc.math cimport exp from libc.math cimport log, exp from libc.stdlib cimport rand, RAND_MAX import cython #%% N=500 graph = initUniformRandomGraph(N) from graph_tool.spectral import adjacency x=crandint(0,N-1) y=crandint(0,N-1) mat = adjacency(graph).tolil() rows = mat.rows.copy() #%% %timeit np.random.choice(graph.get_all_neighbors(x)) %timeit graph.get_all_neighbors(x)[crandint(0, graph.get_out_degrees([x])[0]-1)] %timeit np.random.choice(graph.get_out_neighbors(x)) %timeit graph.get_out_neighbors(x)[crandint(0, graph.get_out_degrees([x])[0]-1)] %timeit np.random.choice(rows[x]) %timeit rows[x][crandint(0, graph.get_out_degrees([x])[0]-1)] # %% %timeit graph.get_all_neighbors(x) %timeit adjacency(graph).tolil().rows[x]
