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IsomorphismChecksUpdated.py
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IsomorphismChecksUpdated.py
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import networkx as nx
from networkx.algorithms import isomorphism
import networkx.algorithms.isomorphism as iso
#Checks if the sets of vertex labels are same, for two edges
def checkTupleEquality(tuple_a,tuple_b):
if tuple_a[0]==tuple_b[0] and tuple_a[1]==tuple_b[1]:
return True
elif tuple_a[0]==tuple_b[1] and tuple_a[1]==tuple_b[0]:
return True
else:
return False
def nodeMatchWithVertexLabels(dictA,dictB):
#Debug Statement to see if function is entered
#print "blah"
return checkTupleEquality(dictA['label'],dictB['label'])
def findCommonNode(tuple_a,tuple_b):
for i in tuple_a:
if i in tuple_b:
return i
def generateLabeledLineGraph(G):
lineGraph=nx.line_graph(G)
for vertexIndex in lineGraph:
lineGraph.node[vertexIndex]['label']=(G.node[vertexIndex[0]]['label'],G.node[vertexIndex[1]]['label'])
for n,nbrsdict in lineGraph.adjacency_iter():
for nbr,eattr in nbrsdict.items():
lineGraph.edge[n][nbr]['label']=G.node[findCommonNode(n,nbr)]['label']
return lineGraph
em = iso.categorical_edge_match('label', 'miss')
def checkSubGraphIsomorphismWithLabels(G1,G2):
if len(G1.nodes())==2 and len(G1.edges())==1:
loneEdge=G1.edges()[0]
loneEdgetuple=(G1.node[loneEdge[0]]['label'],G1.node[loneEdge[1]]['label'])
foundMatch=False
for edge in G2.edges():
edgeLabel=(G2.node[edge[0]]['label'],G2.node[edge[1]]['label'])
if not foundMatch:
foundMatch=checkTupleEquality(edgeLabel,loneEdgetuple)
print foundMatch
return foundMatch
#Returns true if G1 is a subGraph of G2
lineGraphG1=generateLabeledLineGraph(G1)
lineGraphG2=generateLabeledLineGraph(G2)
GM=isomorphism.GraphMatcher(lineGraphG2,lineGraphG1,node_match=nodeMatchWithVertexLabels,edge_match=em)
#GM=isomorphism.GraphMatcher(lineGraphG2,lineGraphG1,node_match=nodeMatchWithVertexLabels)
return GM.subgraph_is_isomorphic()
def generateIndependentEmbeddings(G1,G2):
if len(G1.nodes())==2 and len(G1.edges())==1:
embeddings=[]
loneEdge=G1.edges()[0]
loneEdgetuple=(G1.node[loneEdge[0]]['label'],G1.node[loneEdge[1]]['label'])
for edge in G2.edges():
edgeLabel=(G2.node[edge[0]]['label'],G2.node[edge[1]]['label'])
foundMatch=checkTupleEquality(edgeLabel,loneEdgetuple)
if foundMatch:
embedding=[]
embedding.append(edge)
embeddings.append(embedding)
print embeddings
return embeddings
else:
#Returns (one of) the maximal set of independent embeddings of G1 in G2.
embeddings=[]
lineGraphG1=generateLabeledLineGraph(G1)
lineGraphG2=generateLabeledLineGraph(G2)
print lineGraphG1.nodes()
iterations=0
while True:
GM=isomorphism.GraphMatcher(lineGraphG2,lineGraphG1,node_match=nodeMatchWithVertexLabels,edge_match=em)
isSubIso=GM.subgraph_is_isomorphic()
if not isSubIso:
break
edgeToEdgeMapping=GM.mapping
embedding=[]
for key in edgeToEdgeMapping:
lineGraphG2.remove_node(key)
embedding.append(key)
embeddings.append(embedding)
if len(edgeToEdgeMapping.keys())==0:
break
iterations+=1
print embeddings
return embeddings
def findLowerBoundFeature(feature,graph):
embeddings = generateIndependentEmbeddings(feature,graph)
product = 1.0
for embedding in embeddings:
probOfEmbedding = 1.0
for (i,j) in embedding:
probOfEmbedding = probOfEmbedding * graph.edge[i][j]['weight']
product = product * (1-probOfEmbedding)
return (1-product)
G1=nx.Graph()
G1.add_node(1,label="A")
G1.add_node(2,label="B")
G1.add_node(3,label="A")
G1.add_edge(1,2)
G1.add_edge(2,3)
G1.add_edge(1,3)
G2=nx.Graph()
G2.add_node(1,label="A")
G2.add_node(2,label="A")
G2.add_node(3,label="B")
G2.add_edge(1,2)
G2.add_edge(2,3)
G2.add_edge(1,3)
G3=nx.Graph()
G3.add_node(1,label="A")
G3.add_node(2,label="C")
G3.add_node(3,label="B")
G3.add_edge(1,2)
G3.add_edge(2,3)
G3.add_edge(1,3)
G4=nx.Graph()
G4.add_node(1,label="A")
G4.add_node(2,label="A")
G4.add_node(3,label="B")
G4.add_edge(1,2)
G4.add_edge(2,3)
G5=nx.Graph()
G5.add_node(1,label="A")
G5.add_node(2,label="B")
G5.add_edge(1,2)
G10=nx.Graph()
G10.add_node(1,label="A")
G10.add_node(2,label="B")
G10.add_node(3,label="A")
G10.add_edge(1,2)
G10.add_edge(2,3)
G11=nx.Graph()
G11.add_node(1,label="A")
G11.add_node(2,label="B")
G11.add_node(3,label="A")
G11.add_edge(1,2)
G11.add_edge(2,3)
G11.add_edge(1,3)
G12=nx.Graph()
G12.add_node(1,label="A")
G12.add_node(2,label="A")
G12.add_node(3,label="B")
G12.add_node(4,label="B")
G12.add_edge(1,2)
G12.add_edge(2,3)
G12.add_edge(2,4)
G13=nx.Graph()
G13.add_node(1,label="A")
G13.add_node(2,label="A")
G13.add_node(3,label="B")
G13.add_edge(1,2)
G13.add_edge(2,3)
G13.add_edge(1,3)
print checkSubGraphIsomorphismWithLabels(G1,G2)
print checkSubGraphIsomorphismWithLabels(G1,G3)
print checkSubGraphIsomorphismWithLabels(G4,G1)
print checkSubGraphIsomorphismWithLabels(G5,G1)
print checkSubGraphIsomorphismWithLabels(G10,G11)
print checkSubGraphIsomorphismWithLabels(G13,G12)
G14=nx.Graph()
G14.add_node(1,label="A")
G14.add_node(2,label="B")
G14.add_node(3,label="A")
G14.add_edge(1,2)
G14.add_edge(2,3)
G14.add_edge(1,3)
G15=nx.Graph()
G15.add_node(1,label="A")
G15.add_node(2,label="B")
G15.add_node(3,label="A")
G15.add_node(4,label="A")
G15.add_node(5,label="A")
G15.add_node(6,label="B")
G15.add_node(7,label="B")
G15.add_edge(1,2)
G15.add_edge(2,3)
G15.add_edge(1,3)
G15.add_edge(3,4)
G15.add_edge(3,7)
G15.add_edge(4,7)
G15.add_edge(4,5)
G15.add_edge(5,6)
G15.add_edge(4,6)
G16=nx.Graph()
G16.add_node(1,label="A")
G16.add_node(2,label="B")
G16.add_edge(1,2)
G17=nx.Graph()
G17.add_node(1,label="A")
G17.add_node(2,label="B")
G17.add_node(3,label="A")
G17.add_edge(1,2)
G17.add_edge(2,3)
G17.add_edge(1,3)
G18=nx.Graph()
G18.add_node(1,label="A")
G18.add_node(2,label="B")
G18.add_node(3,label="B")
G18.add_edge(1,2)
G18.add_edge(1,3)
G19=nx.Graph()
G19.add_node(1,label="B")
G19.add_node(2,label="A")
G19.add_node(3,label="B")
G19.add_node(4,label="A")
G19.add_edge(1,2)
G19.add_edge(2,3)
G19.add_edge(3,4)
G19.add_edge(4,1)
generateIndependentEmbeddings(G10,G11)
generateIndependentEmbeddings(G14,G15)
generateIndependentEmbeddings(G18,G19)
print checkSubGraphIsomorphismWithLabels(G16,G17)
generateIndependentEmbeddings(G16,G17)
print nx.line_graph(G16).nodes()
print "20-21"
G20=nx.Graph()
G20.add_node(1,label="A")
G20.add_node(2,label="A")
G20.add_edge(1,2)
G21=nx.Graph()
G21.add_node(1,label="B")
G21.add_node(2,label="B")
G21.add_node(3,label="B")
G21.add_edge(1,2)
G21.add_edge(2,3)
checkSubGraphIsomorphismWithLabels(G20,G21)
print generateIndependentEmbeddings(G16,G17)
print generateIndependentEmbeddings(G20,G21)