Making graphs compact by lossless contraction

Abstract

This paper proposes a scheme to reduce big graphs to small graphs. It contracts obsolete parts and regular structures into supernodes. The supernodes carry a synopsis $$S_\mathcal {Q}$$ S Q for each query class $$\mathcal {Q}$$ Q in use, to abstract key features of the contracted parts for answering queries of $$\mathcal {Q}$$ Q . Moreover, for various types of graphs, we identify regular structures to contract. The contraction scheme provides a compact graph representation and prioritizes up-to-date data. Better still, it is generic and lossless. We show that the same contracted graph is able to support multiple query classes at the same time, no matter whether their queries are label based or not, local or non-local. Moreover, existing algorithms for these queries can be readily adapted to compute exact answers by using the synopses when possible and decontracting the supernodes only when necessary. As a proof of concept, we show how to adapt existing algorithms for subgraph isomorphism, triangle counting, shortest distance, connected component and clique decision to contracted graphs. We also provide a bounded incremental contraction algorithm in response to updates, such that its cost is determined by the size of areas affected by the updates alone, not by the entire graphs. We experimentally verify that on average, the contraction scheme reduces graphs by 71.9% and improves the evaluation of these queries by 1.69, 1.44, 1.47, 2.24 and 1.37 times, respectively.