Emergence of Preferential Attachment and Glass-Ceiling Effects in Autonomous Networks of LLMs

2026-07-01

AI Summary

This study investigates the origins of structural inequality in autonomous collaborative networks of large language models (LLMs), revealing how preferential attachment—where stronger agents gain more connections—and a “glass ceiling” effect—where weaker agents paradoxically occupy central positions—coexist. By modeling agent interactions as a temporal directed weighted graph and integrating mean-field dynamics, contraction mapping theory, and a cross-attention–inspired utility function for collaborator selection, the work establishes the first theoretical framework for type-dependent centrality evolution, proving that centrality measures for each agent type converge to a unique stable equilibrium. Experiments with hundreds of agents confirm the persistent emergence of centrality gaps, whose direction and magnitude are shaped by model family, scale, system prompts, and task design; notably, moderate preferential attachment based on alignment capability enhances collective performance.

Abstract

We investigate the emergence of structural disparities in networks of collaborating large language model (LLM) agents. When LLM agents autonomously choose collaborators, the resulting communication network exhibits preferential-attachment dynamics: agents that are already prominent become increasingly likely to attract additional connections. In some cases, weaker LLM agents (agents with smaller base model or older version) can disproportionately occupy central and influential network positions relative to stronger LLM agents. We interpret this as a type-dependent glass-ceiling effect (GCE). We model the network of LLM agents as a time-evolving sequence of directed weighted graphs, where the vector-valued edge weights represent cumulative tokens exchanged, number of interaction rounds, and reasoning effort. Using a contraction mapping argument on the mean-field dynamics, we prove that the importance (centrality) of each agent type converges to a unique stable equilibrium. To ground the model in LLM decision mechanisms, we introduce a cross-attention-inspired utility for collaborator selection. This utility specifies the local connection dynamics and, together with the mean-field model, yields a predictive characterization of the limiting network structure and its type-dependent centrality gaps. To validate the theory, we develop an experimental testbed with 100 LLM agents. Our experiments show that autonomous network formation can generate persistent centrality disparities, with their magnitude and direction depending on model family, model size, system-prompt design, and task context. They further show that the effect of preferential attachment depends on its alignment with model capability: reinforcing it improves collective performance when stronger agents become central, whereas weakening it improves performance when network dynamics instead favor weaker agents.

Problem

• preferential attachment
• glass-ceiling effect
• LLM agents
• network centrality
• structural disparity

Innovation

• preferential attachment
• glass-ceiling effect
• mean-field dynamics
• cross-attention-inspired utility
• autonomous LLM networks