Agent-Based Modelling (ABM) has emerged as an essential tool for simulating social networks, encompassing diverse phenomena such as information dissemination, influence dynamics, and community formation. However, manually configuring varied agent interactions and information flow dynamics poses challenges, often resulting in oversimplified models that lack real-world generalizability. Integrating modern Large Language Models (LLMs) with ABM presents a promising avenue to address these challenges and enhance simulation fidelity, leveraging LLMs' human-like capabilities in sensing, reasoning, and behavior. In this paper, we propose a novel framework utilizing LLM-empowered agents to simulate social network users based on their interests and personality traits. The framework allows for customizable agent interactions resembling various social network platforms, including mechanisms for content resharing and personalized recommendations. We validate our framework using a comprehensive Twitter dataset from the 2020 US election, demonstrating that LLM-agents accurately replicate real users' behaviors, including linguistic patterns and political inclinations. These agents form homogeneous ideological clusters and retain the main themes of their community. Notably, preference-based recommendations significantly influence agent behavior, promoting increased engagement, network homophily and the formation of echo chambers. Overall, our findings underscore the potential of LLM-agents in advancing social media simulations and unraveling intricate online dynamics.