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Graph Matching Networks for Learning the Similarity of Graph Structured Objects (arxiv.org)
117 points by bookofjoe 16 days ago | hide | past | web | favorite | 6 comments

Thanks! Looks quite interesting. Hopefully better seamless GNN support in Julia's FluxML[1].

[1] https://github.com/FluxML/Flux.jl/issues/625

For context, determining if two graphs are isomorphic is NP-complete.

It is already all but known to be quasi-polynomial, thanks to László Babai: https://www.quantamagazine.org/graph-isomorphism-vanquished-...

Graph isomorphism is actually not known to be NP-complete. Many complexity theorists believe it isn't, since if it is, then the polynomial hierarchy collapses.

Also approximate matching via spectral methods is polynomial. You basically take eigendecomposition of graph adjacency matrix and take inner product of eigenvectors, because spectrum is invariant under permutation of node labels. Works well on noise free and large graphs, because you are unlikely to be unlucky enough to land on isospectral graphs.

I'm imagining a number of use cases for something like this in the information security domain but don't know enough about graph theory to chew into this paper. Would it be possible to do something like k-means with this to identify patterns in existing graphs as well?

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