Retrieving Top Weighted Triangles in Graphs

TL;DR

This paper introduces fast deterministic and random sampling algorithms to efficiently identify the top weighted triangles in large weighted graphs, significantly outperforming existing enumeration methods.

Contribution

The paper presents novel scalable algorithms for finding the highest weighted triangles in large weighted graphs, addressing a gap in pattern mining for weighted networks.

Findings

Top-1000 weighted triangles found in 30 seconds on billions of edges

Algorithms outperform existing enumeration schemes by orders of magnitude

Methods enable scalable pattern mining in weighted graphs

Abstract

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of connection between nodes, which are often modeled by a weighted graph, but existing scalable graph algorithms for pattern mining are designed for unweighted graphs. Here, we develop a suite of deterministic and random sampling algorithms that enable the fast discovery of the 3-cliques (triangles) with the largest weight in a graph, where weight is measured by a generalized mean of a triangle's edges. 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 thus open the door towards scalable pattern mining in weighted graphs.