On the Identification of Isomorphic Graphs for Graph Neural Network using Multi-graph Approach

The Graph Isomorphism problem regained interest with the rise of Graph Neural Networks (GNN). These GNN models have limited ability to distinguish between isomorphic graphs and hence their outputs are modified although the inputs remain the same. Bringing a mathematical way to determine the existing isomorphism between graphs will improve GNN performance. We proposed a multi-graph approach that allows us to extract the permutations to perform to recover one graph from the other. We construct a multi-graph from both input graphs and extract pairs of nodes that respect some properties we have defined. From simple and small graphs, we have been able to correctly extract the isomorphism or permutation matrix existing between both graphs. The extension to large graphs remains a challenge as it requires more computations to discard among a large number of possible candidates.