It has been demonstrated that adversarial graphs, i.e., graphs with imperceptible perturbations, can cause deep graph models to fail on classification tasks. In this work, we extend the concept of adversarial graphs to the community detection problem, which is more challenging. We propose novel attack and defense techniques for community detection problem, with the objective of hiding targeted individuals from detection models and enhancing the robustness of community detection models, respectively. These techniques have many applications in real-world scenarios, for example, protecting personal privacy in social networks and understanding camouflage patterns in transaction networks. To simulate interactive attack and defense behaviors, we further propose a game-theoretic framework, called CD-GAME. One player is a graph attacker, while the other player is a Rayleigh Quotient defender. The CD-GAME models the mutual influence and feedback mechanisms between the attacker and the defender, revealing the dynamic evolutionary process of the game. Both players dynamically update their strategies until they reach the Nash equilibrium. Extensive experiments demonstrate the effectiveness of our proposed attack and defense methods, and both outperform existing baselines by a significant margin. Furthermore, CD-GAME provides valuable insights for understanding interactive attack and defense scenarios in community detection problems. We found that in traditional single-step attack or defense, attacker tends to employ strategies that are most effective, but are easily detected and countered by defender. When the interactive game reaches a Nash equilibrium, attacker adopts more imperceptible strategies that can still achieve satisfactory attack effectiveness even after defense.
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