Condensed Graphs: A Generic Framework for Accelerating Subgraph Census Computation

Determining subgraph frequencies is at the core of several graph mining methodologies such as discovering network motifs or computing graphlet degree distributions. Current state-of-the-art algorithms for this task either take advantage of common patterns emerging on the networks or target a set of specific subgraphs for which analytical calculations are feasible. Here, we propose a novel network generic framework revolving around a new data-structure, a Condensed Graph, that combines both the aforementioned approaches, but generalized to support any subgraph topology and size. Furthermore, our methodology can use as a baseline any enumeration based census algorithm, speeding up its computation. We target simple topologies that allow us to skip several redundant and heavy computational steps using combinatorics. We were are able to achieve substantial improvements, with evidence of exponential speedup for our best cases, where these patterns represent up to 97% of the network, from a broad set of real and synthetic networks.