Mining Density Contrast Subgraphs

TL;DR

This paper introduces the concept of Density Contrast Subgraphs (DCS) for comparing two graphs with shared vertices, proposing algorithms to efficiently detect subgraphs with contrasting density, validated by experiments on real datasets.

Contribution

The paper defines DCS for two graphs, proves its computational hardness, and develops efficient algorithms for its detection, addressing a gap in multi-graph dense subgraph mining.

Findings

Algorithms are effective in real-world datasets.

Detection of DCS is computationally hard.

Proposed methods outperform baseline approaches.

Abstract

Dense subgraph discovery is a key primitive in many graph mining applications, such as detecting communities in social networks and mining gene correlation from biological data. Most studies on dense subgraph mining only deal with one graph. However, in many applications, we have more than one graph describing relations among a same group of entities. In this paper, given two graphs sharing the same set of vertices, we investigate the problem of detecting subgraphs that contrast the most with respect to density. We call such subgraphs Density Contrast Subgraphs, or DCS in short. Two widely used graph density measures, average degree and graph affinity, are considered. For both density measures, mining DCS is equivalent to mining the densest subgraph from a "difference" graph, which may have both positive and negative edge weights. Due to the existence of negative edge weights, existing dense subgraph detection algorithms cannot identify the subgraph we need. We prove the computational hardness of mining DCS under the two graph density measures and develop efficient algorithms to find DCS. We also conduct extensive experiments on several real-world datasets to evaluate our algorithms. The experimental results show that our algorithms are both effective and efficient.