Retrieving Top Weighted Triangles in Graphs.

Raunak Kumar, Paul Liu, Moses Charikar, Austin R. Benson

Abstract: Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and there are several methods for scaling subgraph counting to large graphs. Many real-world networks have a notion of strength of connection between nodes, which is often modeled by a weighted graph, but existing scalable algorithms for pattern mining are designed for unweighted graphs. Here, we develop deterministic and random sampling algorithms that enable the fast discovery of the 3-cliques (triangles) of largest weight, as measured by the generalized mean of the triangle's edge weights. For example, one of our proposed algorithms can find the top-1000 weighted triangles of a weighted graph with billions of edges in thirty seconds on a commodity server, which is orders of magnitude faster than existing "fast" enumeration schemes. Our methods open the door towards scalable pattern mining in weighted graphs.