feat:exact topology matching and approximate feature matching

[OrigenesZhang]

Changes made to networkx's implementation for VF2 algorithm to support approximate matching on nodes' features.

Heuristics made on topology matching:

• Starting the search with the node pairs with the most similar node embeddings (from cosine similarity perspective)
• Letting node pairs with very similar node embeddings pass the syntactic feasibility test directly (threshold passed in as an argument of the class constructor)

Example:

from vf2 import GraphMatcher
from torch import Tensor
from torch_geometric.utils import from_networkx

import networkx as nx

G1 = nx.Graph()
for i in range(4):
    G1.add_node(i)
for i in range(3):
    G1.add_edge(i, i+1)
    
G2 = nx.Graph()
for i in range(3):
    G2.add_node(i)
for i in range(2):
    G2.add_edge(i, i+1)

G1 = from_networkx(G1)
G2 = from_networkx(G2)

e1 = Tensor([[1, 1], [2, 2], [3, 3], [4, 4]])
e2 = Tensor([[1, 2], [3, 4], [5, 6]])

fv1 = Tensor([[1, 1], [1, 2], [1, 3], [1, 4]])
fv2 = Tensor([[1, 1], [1, 3], [1, 4]])


GM = GraphMatcher(G1, G2, e1, e2, fv1, fv2, 0.3, 0)
print(GM.subgraph_is_isomorphic())
print(GM.mapping)  # node index in G1 (target graph) to node index in G2 (query graph)

GM = GraphMatcher(G1, G2, e1, e2, fv1, fv2, 0.01, 0)
print(GM.subgraph_is_isomorphic())

Expected output:

True
{2: 0, 1: 1, 0: 2}
False

[OrigenesZhang]

This could be improved with a top K search?

[mjyoussef]

Yes