Network topology shapes consensus and vulnerability in LLM populations

As large language models (LLMs) are deployed in interacting populations, their collective behaviour depends not only on the models but also on who interacts with whom. Studies of convention formation in LLM populations have mainly tested well-mixed interactions. We place policies extracted from four LLMs on fully connected, random regular, and heterogeneous networks, with $10^3$ to $10^5$ agents playing the naming game. Topology affects how quickly consensus emerges, sometimes whether it emerges at all, and, in rare cases, which convention wins. Sparsest networks slow consensus up to twelvefold. Yet, by preserving correlations between persistent neighbours, they restore consensus in some cases that fail to converge under well-mixed interactions. Networks also govern vulnerability to adversarial attack. We measure the critical mass of committed agents needed to overturn an established convention. Tipping thresholds follow the same ordering across models and conditions: hubs $\leq$ random $\leq$ low-degree nodes. On the most heterogeneous topology, median critical masses are 3%, 16%, and 35%, respectively; targeting hubs requires one-sixth as many committed agents as random placement. For most models, networked populations are easier to tip than well-mixed ones, so well-mixed estimates can overstate robustness. Assessing the safety of multi-agent AI requires mapping who interacts with whom.