Detection of large exact subgraph isomorphisms with a topology-only graphlet index built using deterministic walks

Abstract: We introduce the first algorithm to perform topology-only local graph matching (a.k.a. local network alignment or subgraph isomorphism): BLANT, for Basic Local Alignment of Network Topology. BLANT first creates a limited, high-specificity index of a single graph containing connected k-node induced subgraphs called k-graphlets, for k=6-15. The index is constructed in a deterministic way such that, if significant common network topology exists between two networks, their indexes are likely to overlap. This is the key insight which allows BLANT to discover alignments using only topological information. To align two networks, BLANT queries their respective indexes to form large, high quality local alignments. BLANT is able to discover highly topologically similar alignments (S3 >= 0.95) of up to 150 node-pairs for which up to 50% of node pairs differ from their "assigned" global counterpart. These results compare favorably against the baseline, a state-of-the-art local alignment algorithm which was adapted to be topology-only. Such alignments are 3x larger and differ 30% more (additive) more from the global alignment than alignments of similar topological similarity (S3 >= 0.95) discovered by the baseline. We hope that such regions of high local similarity and low global similarity may provide complementary insights to global alignment algorithms.