Network topology shapes consensus and vulnerability in LLM populations
Abstract
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 103 to 105 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 ≤ random ≤ 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.
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BibTeX
@misc{passaro2026network,
title = {{Network topology shapes consensus and vulnerability in LLM populations}},
author = {Roberto Passaro and Ariel Flint and Romualdo Pastor-Satorras and Andrea Baronchelli and Luca Maria Aiello},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31165},
eprint = {2610.31165},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31165},
}
RIS
TY - UNPB
TI - Network topology shapes consensus and vulnerability in LLM populations
AU - Roberto Passaro
AU - Ariel Flint
AU - Romualdo Pastor-Satorras
AU - Andrea Baronchelli
AU - Luca Maria Aiello
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31165
UR - https://arxiv.org/abs/2610.31165
AB - 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 ≤ random ≤ 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.
ER -