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Fize Jacques authored8af775b6
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# coding = utf-8
import networkx as nx
import numpy as np
import scipy.sparse
class DeltaCon0():
__type__ = "sim"
@staticmethod
def compare(list_gs,selected):
n=len(list_gs)
comparison_matrix = np.zeros((n,n))
for i in range(n):
for j in range(i,n):
g1,g2=list_gs[i],list_gs[j]
f=True
if not list_gs[i] or not list_gs[j]:
f=False
elif len(list_gs[i])== 0 or len(list_gs[j]) == 0:
f=False
if selected:
if not i in selected:
f=False
if f:
# S1
epsilon = 1/(1+DeltaCon0.maxDegree(g1))
D, A = DeltaCon0.degreeAndAdjacencyMatrix(g1)
S1 = np.linalg.inv(np.identity(len(g1))+(epsilon**2)*D -epsilon*A)
# S2
D, A = DeltaCon0.degreeAndAdjacencyMatrix(g2)
epsilon = 1 / (1 + DeltaCon0.maxDegree(g2))
S2 = np.linalg.inv(np.identity(len(g2))+(epsilon**2)*D -epsilon*A)
comparison_matrix[i,j] = 1/(1+DeltaCon0.rootED(S1,S2))
comparison_matrix[j,i] = comparison_matrix[i,j]
else:
comparison_matrix[i, j] = 0.
comparison_matrix[j, i] = comparison_matrix[i, j]
return comparison_matrix
@staticmethod
def rootED(S1,S2):
return np.sqrt(np.sum((S1-S2)**2)) # Long live numpy !
@staticmethod
def degreeAndAdjacencyMatrix(G):
"""
Return the Degree(D) and Adjacency Matrix(A) from a graph G.
Inspired of nx.laplacian_matrix(G,nodelist,weight) code proposed by networkx
:param G:
:return:
"""
A = nx.to_scipy_sparse_matrix(G, nodelist=list(G.nodes), weight="weight",
format='csr')
n, m = A.shape
diags = A.sum(axis=1)
D = scipy.sparse.spdiags(diags.flatten(), [0], m, n, format='csr')
return D, A
@staticmethod
def maxDegree(G):
degree_sequence = sorted(nx.degree(G).values(), reverse=True) # degree sequence
# print "Degree sequence", degree_sequence
dmax = max(degree_sequence)
return dmax
class DeltaCon():
__type__ = "sim"
@staticmethod
def relabel_nodes(graph_list):
label_lookup = {}
label_counter = 0
n= len(graph_list)
# label_lookup is an associative array, which will contain the
# mapping from multiset labels (strings) to short labels
# (integers)
for i in range(n):
nodes = list(graph_list[i].nodes)
for j in range(len(nodes)):
if not (nodes[j] in label_lookup):
label_lookup[nodes[j]] = label_counter
label_counter += 1
graph_list[i] = nx.relabel_nodes(graph_list[i], label_lookup)
return graph_list
@staticmethod
def compare(list_gs, g=3):
n=len(list_gs)
list_gs=DeltaCon.relabel_nodes(list_gs)
comparison_matrix = np.zeros((n,n))
for i in range(n):
for j in range(i,n):
g1,g2=list_gs[i],list_gs[j]
V = list(g1.nodes)
V.extend(list(g2.nodes))
V=np.unique(V)
partitions=V.copy()
np.random.shuffle(partitions)
if len(partitions)< g:
partitions=np.array([partitions])
else:
partitions=np.array_split(partitions,g)
partitions_e_1 = DeltaCon.partitions2e(partitions, list(g1.nodes))
partitions_e_2 = DeltaCon.partitions2e(partitions, list(g2.nodes))
S1,S2=[],[]
for k in range(len(partitions)):
s0k1,s0k2=partitions_e_1[k],partitions_e_2[k]
# S1
epsilon = 1/(1+DeltaCon0.maxDegree(g1))
D, A = DeltaCon0.degreeAndAdjacencyMatrix(g1)
s1k = np.linalg.inv(np.identity(len(g1))+(epsilon**2)*D -epsilon*A)
s1k=np.linalg.solve(s1k,s0k1).tolist()
# S2
D, A = DeltaCon0.degreeAndAdjacencyMatrix(g2)
epsilon = 1 / (1 + DeltaCon0.maxDegree(g2))
s2k= np.linalg.inv(np.identity(len(g2))+(epsilon**2)*D -epsilon*A)
s2k = np.linalg.solve(s2k, s0k2).tolist()
S1.append(s1k)
S2.append(s2k)
comparison_matrix[i,j] = 1/(1+DeltaCon0.rootED(np.array(S1),np.array(S2)))
comparison_matrix[j,i] = comparison_matrix[i,j]
return comparison_matrix
@staticmethod
def partitions2e( partitions, V):
e = [ [] for i in range(len(partitions))]
for p in range(len(partitions)):
e[p] = []
for i in range(len(V)):
if i in partitions[p]:
e[p].append(1.0)
else:
e[p].append(0.0)
return e