Hallucination is a critical reliability challenge in multi-agent Large Language Model (LLM) systems because unsupported claims can propagate through recursive interactions and produce collective false consensus. We model collective hallucination as a time-evolving network process over directed communication graphs and introduce HPR-Adaptive, a defense framework combining dynamic trust weighting, external claim verification, propagation-aware interaction regulation, and selective isolation of unreliable agents. We evaluate HPR-Adaptive on 1,317 TruthfulQA and TriviaQA queries using a heterogeneous six-agent system across five recursive reasoning rounds and multiple communication topologies. Compared with undefended multi-agent reasoning, HPR-Adaptive reduces hallucination rate from 0.118 to 0.072 (39.0%), while increasing factual accuracy from 0.812 to 0.867 and semantic consistency from 0.784 to 0.836. It also lowers the hallucination amplification factor from 1.34 to 1.08, increases propagation resistance from 0.882 to 0.928, and reduces the effective reproduction number from 1.08 to 0.81, shifting the system from self-sustaining propagation to controlled attenuation. Scale-free networks show the strongest cascading behavior without defense, with an amplification factor of 1.45 and reproduction number of 1.21; HPR-Adaptive reduces these to 1.12 and 0.92, respectively. These results show that propagation-aware control can substantially improve the factual reliability and stability of recursive multi-agent LLM systems.

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