Adversarial Optimization of the $\delta$-TriBound Objective for Robust Community Detection Attacks Across Multiple Graphs

Abstract

Adversarial attacks on community detection (CD) have attracted increasing attention due to CD’s importance in numerous applications and its privacy implications. While existing studies have demonstrated the effectiveness of adversarial perturbations in degrading CD performance, most prior attacks are restricted to single-graph settings. This limitation contrasts with the growing adoption of multigraph CD frameworks, where community structures are inferred from multiple heterogeneous or cross-platform graphs. Moreover, existing attack methods suffer from two fundamental weaknesses: 1) proxy metrics neglect community structures; and 2) lacking budget allocation ability and the capability to handle multiple graphs simultaneously. To address these challenges, we propose a new research problem, multigraph perturbation for community detection via $\delta$-TriBound minimization ($\delta$-MPCD). At the core of our formulation is $\delta$-TriBound, a proxy metric designed to capture higher-order triangle patterns anchoring community cohesion and to enable effective adversarial perturbations across multiple graphs. We theoretically justify the utility of $\delta$-TriBound, prove that $\delta$-MPCD is NP-hard, and design a $({1}/{24})$-approximation algorithm, multiple graph $\delta$-TriBounds minimization with edge addition ($\delta$-MGMA). Extensive experiments on real-world datasets demonstrate that our method consistently degrades community detection performance across diverse CD algorithms in multigraph settings, significantly outperforming state-of-the-art baselines.