def test_normalized_laplacian_spectrum(self):
"Normalized Laplacian eigenvalues"
evals = numpy.array([0, 0, 0.7712864461218, 1.5, 1.7287135538781])
e = sorted(nx.normalized_laplacian_spectrum(self.G))
npt.assert_almost_equal(e, evals)
e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight=None))
npt.assert_almost_equal(e, evals)
e = sorted(nx.normalized_laplacian_spectrum(self.WG))
npt.assert_almost_equal(e, evals)
e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight='other'))
npt.assert_almost_equal(e, evals)
def cut(graph):
if (len(graph.nodes) < 2):
return list(graph.nodes)
laplacian = nx.normalized_laplacian_matrix(graph).toarray()
eignvector = np.linalg.eigh(laplacian)[1][:, 1]
eignvalues = nx.normalized_laplacian_spectrum(graph)
#print("The second smallest eignvalue: {0}\nEignvector: {1}".format(result[0][1], eignvector))
print("Eignvalues {0}".format(eignvalues))
print("Eignvector {0}".format(eignvector))
histogram = np.histogram(eignvalues,
bins=np.size(eignvalues),
density=True)
if len(eignvalues) > 2:
ratio = eignvalues[2] - eignvalues[1]
else:
ratio = eignvalues[1] - eignvalues[1]
print("Ratio {0:.2f}".format(ratio))
threshold = 0 #np.mean(eignvector)
res = input("Divide?")
if res == 'n': #(ratio < 0.06) :#((eignvector < threshold).all() or (eignvector >= threshold).all()) or (len(graph.nodes) <= 2): #len(graph.nodes) <= 2
return list(graph.nodes)
else:
sub1 = graph.copy()
sub2 = graph.copy()
sub1.remove_nodes_from(
np.array(list(graph.nodes))[(eignvector < threshold)])
sub2.remove_nodes_from(
np.array(list(graph.nodes))[(eignvector >= threshold)])
return [cut(sub1), cut(sub2)]
def computeFeatures(self, G, features_nx, features_nk):
if("effective_graph_resistance" in features_nx or "nb_spanning_trees" in features_nx or "algebraic_connectivity" in features_nx):
if(self.params["verbose"]):
print("Computing laplacian_eigenvalues")
s = time.time()
self.eigenvalues["laplacian"] = np.real(nx.laplacian_spectrum(G))
if(self.params["verbose"]):
print("Finish laplacian_eigenvalues (%s)" % (timeFormat(time.time()-s)))
if("largest_eigenvalue" in features_nx or "symmetry_ratio" in features_nx or "natural_connectivity" in features_nx):
if(self.params["verbose"]):
print("Computing adjacency_eigenvalues")
s = time.time()
self.eigenvalues["adjacency"] = np.real(nx.adjacency_spectrum(G))
if(self.params["verbose"]):
print("Finish adjacency_eigenvalues (%s)" % (timeFormat(time.time()-s)))
if("weighted_spectrum_3" in features_nx or "weighted_spectrum_4" in features_nx):
if(self.params["verbose"]):
print("Computing normalized_laplacian_eigenvalues")
s = time.time()
self.eigenvalues["normalized_laplacian"] = np.real(nx.normalized_laplacian_spectrum(G))
if(self.params["verbose"]):
print("Finish normalized_laplacian_eigenvalues (%s)" % (timeFormat(time.time()-s)))
return(NodesFeatures.computeFeatures(self, G, features_nx, features_nk))
def weighted_spectrum(G, nodes, n=3, eigenvalues=None):
normalized_laplacian_eigenvalues = None
if(not eigenvalues is None):
normalized_laplacian_eigenvalues = eigenvalues["normalized_laplacian"]
if(normalized_laplacian_eigenvalues is None):
normalized_laplacian_eigenvalues = np.real(nx.normalized_laplacian_spectrum(G))
ws = np.sum((1-normalized_laplacian_eigenvalues)**n)
return(np.float64(ws))
N = 15
g = regular_2D_lattice(N)
g2 = regular_2D_lattice_8_neighbors(N)
#g2 = random_edge_suppression(N,5*N)
G2 = g2.to_networkx().to_undirected()
L2 = nx.normalized_laplacian_matrix(G2)
e = numpy.linalg.eigvals(L2.A)
fig, ax = plt.subplots()
s = np.sort(e)
l, = plt.plot(
np.sort(nx.normalized_laplacian_spectrum(g.to_networkx().to_undirected())))
l, = plt.plot(np.sort(e), lw=2)
ax = plt.axis([0, len(e), -0.5, np.max(e) * 1.5])
axamp = plt.axes([0.25, .03, 0.50, 0.02])
axamp2 = plt.axes([0.25, 0, 0.50, 0.02])
# Slider
samp = Slider(axamp, ' + b on diag', -1.5, 1.5, valinit=0)
samp2 = Slider(axamp2, 'Theta', -.5, 1.5, valinit=1)
def update(val):
# amp is the current value of the slider
amp = samp.val
def laplacian_spectrum(self, ):
return nx.normalized_laplacian_spectrum(self.undirected_g)
def normalized_laplacian_spectrum(play: dict):
G = nx.Graph(big_umat_df(play))
res = nx.normalized_laplacian_spectrum(G)
return res