Cohesive Group Discovery in Interaction Graphs under Explicit Density Constraints

TL;DR

This paper introduces EDQC, a new framework for discovering cohesive groups in interaction graphs with explicit density constraints, outperforming existing methods in size, variance, and robustness across real-world data.

Contribution

EDQC is a novel, efficient framework that combines energy diffusion and refinement techniques to reliably find large, density-constrained quasi-cliques in real-world graphs.

Findings

EDQC finds the largest mean $$-quasi-cliques in most tested graphs.

EDQC achieves lower variance than state-of-the-art methods.

EDQC significantly outperforms baselines in robustness and utility.

Abstract

Discovering cohesive groups is a fundamental primitive in graph-based recommender systems, underpinning tasks such as social recommendation, bundle discovery, and community-aware modeling. In interaction graphs, cohesion is often modeled as the $\gamma$-quasi-clique, an induced subgraph whose internal edge density meets a user-defined threshold $\gamma$. This formulation provides explicit control over within-group connectivity while accommodating the sparsity inherent in real-world data. This paper presents EDQC, an effective framework for cohesive group discovery under explicit density constraints. EDQC leverages a lightweight energy diffusion process to rank vertices for localizing promising candidate regions. Guided by this ranking, the framework extracts and refines a candidate subgraph to ensure the output strictly satisfies the target density requirement. Extensive experiments on 75 real-world graphs across varying density thresholds demonstrate that EDQC identifies the largest mean $\gamma$-quasi-cliques in the vast majority of cases, achieving lower variance than the state-of-the-art methods while maintaining competitive runtime. Furthermore, statistical analysis confirms that EDQC significantly outperforms the baselines, underscoring its robustness and practical utility for cohesive group discovery in graph-based recommender systems.