Finding dense subgraphs with maximum weighted triangle density

Abstract

Finding dense subgraphs from sparse graphs is a fundamental graph mining task that has been applied in various domains, such as social networks, biology, and spam detection. Because the standard formulation of this problem is difficult to solve owing to connections with the Maximum Clique Problem, some tractable formulations have been proposed. These formulations find a dense subgraph by optimizing some density function, such as the degree density or triangle density. In this paper, we introduce the weighted k-clique density, a novel formulation for dense subgraph extraction. We show that the problem of maximizing weighted k-clique density can be solved optimally in polynomial time by solving a series of minimum cut problems. For scalability, we also propose a more efficient greedy algorithm with performance guarantee. The experimental results on real-world network datasets show that, compared with established state-of-the-art algorithms, the proposed algorithm can find a much denser subgraph in terms of edge density and triangle density.