[2603.00121] Graph-theoretic Agreement Framework for Multi-agent LLM Systems

Computer Science > Multiagent Systems arXiv:2603.00121 (cs) [Submitted on 23 Feb 2026] Title:Graph-theoretic Agreement Framework for Multi-agent LLM Systems Authors:Muhammad Umar Javed View a PDF of the paper titled Graph-theoretic Agreement Framework for Multi-agent LLM Systems, by Muhammad Umar Javed View PDF HTML (experimental) Abstract:The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperati...