Large language models (LLMs) have empowered nodes within multi-agent networks with intelligence, showing growing applications in both academia and industry. However, how to prevent these networks from generating malicious information remains unexplored with previous research on single LLM's safety be challenging to transfer. In this paper, we focus on the safety of multi-agent networks from a topological perspective, investigating which topological properties contribute to safer networks. To this end, we propose a general framework, NetSafe along with an iterative RelCom interaction to unify existing diverse LLM-based agent frameworks, laying the foundation for generalized topological safety research. We identify several critical phenomena when multi-agent networks are exposed to attacks involving misinformation, bias, and harmful information, termed as Agent Hallucination and Aggregation Safety. Furthermore, we find that highly connected networks are more susceptible to the spread of adversarial attacks, with task performance in a Star Graph Topology decreasing by 29.7%. Besides, our proposed static metrics aligned more closely with real-world dynamic evaluations than traditional graph-theoretic metrics, indicating that networks with greater average distances from attackers exhibit enhanced safety. In conclusion, our work introduces a new topological perspective on the safety of LLM-based multi-agent networks and discovers several unreported phenomena, paving the way for future research to explore the safety of such networks.
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