Node Similarity with q-Grams for Real-World Labeled Networks
Roberto Grossi (University of Pisa); Alessio Conte (University of Pisa); Gaspare Ferraro (University of Pisa); Andrea Marino (University of Pisa); Kunihiko Sadakane (University of Tokyo); Takeaki Uno (National Institute of Informatics, Japan)
We study node similarity in labeled networks, using the label sequences found in paths of bounded length q leading to the nodes. (This recalls the q-grams employed in document resemblance, based on the Jaccard distance.) When applied to networks, the challenge is two-fold: the number of q-grams generated from labeled paths grows exponentially with q, and their frequency should be taken into account: this leads to a variation of the Jaccard index known as Bray-Curtis index for multisets. We describe nSimGram, a suite of fast algorithms for node similarity with q-grams, based on a novel blend of color coding, probabilistic counting, sketches, and string algorithms, where the universe of elements to sample is exponential. We provide experimental evidence that our measure is effective and our running times scale to deal with large real-world networks.