[Paper Review] Emergence of Scale-Free Networks in Social Interactions among Large Language Models

Giordano De Marzo, L. Pietronero+1 more|arXiv (Cornell University)|Dec 11, 2023

Opinion Dynamics and Social Influence4 citations

TL;DR

This study demonstrates that generative agents powered by GPT-3.5-turbo spontaneously form scale-free networks through social interactions, mirroring human online behavior. The emergence of power-law degree distributions (exponent α = 1.93 ± 0.12) and linear preferential attachment confirms that LLM-driven agents replicate collective network structures seen in real social media, provided token distribution biases are mitigated via agent renaming.

ABSTRACT

Scale-free networks are one of the most famous examples of emergent behavior and are ubiquitous in social systems, especially online social media in which users can follow each other. By analyzing the interactions of multiple generative agents using GPT3.5-turbo as a language model, we demonstrate their ability to not only mimic individual human linguistic behavior but also exhibit collective phenomena intrinsic to human societies, in particular the emergence of scale-free networks. We discovered that this process is disrupted by a skewed token prior distribution of GPT3.5-turbo, which can lead to networks with extreme centralization as a kind of alignment. We show how renaming agents removes these token priors and allows the model to generate a range of networks from random networks to more realistic scale-free networks.

Motivation & Objective

• To investigate whether generative agents powered by LLMs can self-organize into complex network structures resembling real-world social networks.
• To determine if LLM-driven agents exhibit linear preferential attachment, a hallmark of scale-free network formation.
• To examine how model-specific biases—particularly skewed token priors in GPT-3.5-turbo—affect network topology and centrality.
• To evaluate whether renaming agents can mitigate alignment-induced distortions and restore realistic network emergence.
• To assess the suitability of LLMs for use in Agent-Based Models requiring accurate representation of collective human behavior.

Proposed method

• Agents were modeled as generative agents using GPT-3.5-turbo, each initialized with a prompt simulating a social media user and degree information of existing users.
• At each timestep, a new agent was instantiated and prompted to select m existing users to connect with, based on their current degree and social behavior.
• Network growth was simulated iteratively, with connections updated after each agent’s decision, forming a growing network up to N = 2000 nodes.
• The degree distribution was analyzed via complementary cumulative distribution functions (CCDF) in log-log plots to detect power-law behavior.
• Preferential attachment was quantified by computing cumulative attachment probability Π(k), with quadratic growth indicating linear preferential attachment.
• Token prior bias was investigated by comparing networks with and without agent renaming, which disrupted biased word generation patterns.

Experimental results

Research questions

• RQ1 Can generative agents driven by LLMs spontaneously form scale-free networks resembling real online social networks?
• RQ2 Do LLM-powered agents exhibit linear preferential attachment, the mechanism underlying scale-free network formation?
• RQ3 How does the token prior distribution in GPT-3.5-turbo affect the emergence of network structure and centrality?
• RQ4 Can renaming agents mitigate alignment-induced biases and restore realistic network topology?
• RQ5 To what extent can LLMs replicate the full distribution of human social behavior in collective settings, beyond isolated responses?

Key findings

• Generative agents using GPT-3.5-turbo spontaneously form scale-free networks with a power-law degree distribution, as indicated by a CCDF with a slope consistent with a power-law exponent of α = 1.93 ± 0.12.
• The cumulative attachment probability Π(k) exhibits quadratic growth with degree k, confirming linear preferential attachment in the network formation process.
• A skewed token prior in GPT-3.5-turbo leads to extreme network centralization, disrupting realistic scale-free topology.
• Renaming agents effectively removes token prior biases, enabling the model to generate networks ranging from random to realistic scale-free structures.
• The network topology formed by LLM-driven agents closely matches real-world social networks, with a power-law exponent near -2, consistent with Zipf’s law and observed on platforms like Twitter.
• LLMs can replicate not only isolated human-like responses but also the full distribution of social behaviors necessary for valid Agent-Based Modeling.