Scaling Up Structural Clustering to Large Probabilistic Graphs Using Lyapunov Central Limit Theorem

Abstract

Structural clustering is one of the most widely used graph clustering frameworks. In this paper, we focus on structural clustering of probabilistic graphs, which comes with significant computational challenges and has, so far, resisted efficient solutions that are able to scale to large graphs, e.g. the state-of-art can only handle graphs with a few million edges. We address the main bottleneck step of probabilistic structural clustering, computing the structural similarity of vertices based on their Jaccard similarity over the set of possible worlds of a given probabilistic graph. The state-of-art used Dynamic Programming, a quadratic run-time algorithm, that does not scale to pairs of vertices of high degree. In this paper we present a novel approach based on Lyapunov Central Limit Theorem. By using a carefully chosen set of random variables we are able to cast the computation of structural similarity to computing a one-tailed area under the Normal Distribution. Our approach has linear runtime as opposed to quadratic, and as such, it scales to much larger inputs. Extensive experiments show that our approach can handle massive graphs at web-scale which the state-of-art cannot.