Purdue University, USA Social networks shape opinions, behaviors, and information dissemination in human societies. As large language models (LLMs) increasingly integrate into social and professional environments, understanding their behavior within the context of social interactions and networks becomes essential. Our study analyzes LLMs' network formation behavior to examine whether the dynamics of multiple LLMs are similar to or different from human social dynamics. We observe that LLMs exhibit key social network principles, including preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon, when asked about their preferences in network formation. We also investigate LLMs' decision-making based on real-world networks, revealing that triadic closure and homophily have a stronger influence than preferential attachment and that LLMs perform well in network formation predictions. Overall, our study opens up new possibilities for using LLMs in network science research and helps develop socially aware LLMs by shedding light on their social interaction behaviors and exploring their impacts on social dynamics. INTRODUCTION Recent progress in large language models (LLMs), such as GPT [39] and Llama 2 [47], have shown promising developments in AI techniques and their integration into real-life applications. It is thus crucial to comprehend AI actions to ensure they align with human expectations, mitigate potential risks, and maximize their benefits. Misaligned AI actions may lead to unintended consequences, such as biased decision-making, fairness issues, and the miscoordinative or non-cooperative behavior [45]. Recently, researchers have started to apply social science methodologies, such as methods analogous to laboratory experiments [1, 22, 32, 50], agent-based modeling [16, 17, 19, 21, 43, 44], and qualitative methods, to study LLMs. These methods not only reveal the capabilities and interpretability of LLMs but also suggest their potential for applications in social science [12, 22, 28, 42]. In human societies, social networks play a crucial role in shaping individual behaviors, preferences, and connections, as well as influencing the diffusion of information and norms across communities [3, 4, 18, 46, 53]. LLMs have shown great potential in social contexts, notably as intelligent personal assistants that facilitate social and prosocial interactions (see, e.g., [13, 41, 50]).

How can individuals exchange information to learn from each other despite their privacy needs and security concerns? For example, consider individuals deliberating a contentious topic and being concerned about divulging their private experiences. Preserving individual privacy and enabling efficient social learning are both important desiderata but seem fundamentally at odds with each other and very hard to reconcile. We do so by controlling information leakage using rigorous statistical guarantees that are based on differential privacy (DP). Our agents use log-linear rules to update their beliefs after communicating with their neighbors. Adding DP randomization noise to beliefs provides communicating agents with plausible deniability with regard to their private information and their network neighborhoods. We consider two learning environments one for distributed maximum-likelihood estimation given a finite number of private signals and another for online learning from an infinite, intermittent signal stream. Noisy information aggregation in the finite case leads to interesting tradeoffs between rejecting low-quality states and making sure all high-quality states are accepted in the algorithm output. Our results flesh out the nature of the trade-offs in both cases between the quality of the group decision outcomes, learning accuracy, communication cost, and the level of privacy protections that the agents are afforded.