No abstract

Truss decomposition is a popular notion of hierarchical dense substructures in graphs. In a nutshell, k -truss is the largest subgraph in which every edge is contained in at least k triangles. Truss decomposition aims to compute k -trusses for each possible value of k . There are many works that study truss decomposition in deterministic graphs. However, in probabilistic graphs, truss decomposition is significantly more challenging and has received much less attention; state-of-the-art approaches do not scale well to large probabilistic graphs. Finding the tail probabilities of the number of triangles that contain each edge is a critical challenge of those approaches. This is achieved using dynamic programming which has quadratic run-time and thus not scalable to real large networks which, quite commonly, can have edges contained in many triangles (in the millions). To address this challenge, we employ a special version of the Central Limit Theorem (CLT) to obtain the tail probabilities efficiently. Based on our CLT approach we propose a peeling algorithm for truss decomposition that scales to large probabilistic graphs and offers significant improvement over state-of-the-art. We also design a second method which progressively tightens the estimate of the truss value of each edge and is based on h -index computation. In contrast to our CLT-based approach, our h -index algorithm (1) is progressive by allowing the user to see near-results along the way, (2) does not sacrifice the exactness of final result, and (3) achieves all these while processing only one edge and its immediate neighbors at a time, thus resulting in smaller memory footprint. We perform extensive experiments to show the scalability of both of our proposed algorithms.