How Communication Topology Density Shapes Performance in LLM-Based Multi-Agent Systems

Communication topology is a key design variable in LLM-based multi-agent reasoning. Prior work has shown that sparse communication can outperform full connectivity, but the mechanisms linking communication density and degree allocation to performance remain incompletely understood. We propose a method for analyzing how communication topology affects multi-agent reasoning performance. It first exactly decomposes per-round changes in agent-level answer information into corrective gain and misleading loss, then introduces a graph-based propagation model of evidence coverage, error dilution, and same-direction error reinforcement. Under homogeneous fixed-state assumptions, we derive an explicit optimality condition for communication density and show when it has a unique interior solution: corrective gain increases with diminishing returns, whereas misleading loss reflects a competition between error dilution and same-direction error reinforcement. Under a fixed edge budget and the stated homogeneity assumptions, regular or near-regular degree allocations maximize predicted performance among feasible graphs without isolated nodes. Experiments with two open-source models on six reasoning datasets provide qualitative support: the best accuracy among tested conditions occurs at an intermediate density in all 12 model–dataset combinations, and a fixed-budget comparison favors balanced degrees. Together, these results provide a mechanistic basis for communication-topology design.