The Impact of Social Attractiveness on Casual Group Formation: Power-Law Group Sizes and Suppressed Percolation

Abstract: The dynamics of casual group formation has long been a subject of interest in social sciences. While early stochastic models offered foundational insights into group size distributions, they often simplified individual behaviors and lacked mechanisms for heterogeneous social appeal. Here, we re-examine the attractiveness-driven interaction model, an agent-based framework where point-like agents move randomly in a 2D arena and exhibit varied social appeal, leading them to pause near highly attractive celebrity peers. We compare this model to a null model where the agents are continuously in movement, which resembles a Random Geometric Graph. Our extensive simulations reveal significant structural and dynamic differences: unlike the null model, the attractiveness-driven model's average degree increases linearly with system size for fixed density, resulting in more compact groups and the suppression of a percolation transition. Crucially, while the null model's group size distribution is either exponentially decaying or bimodal, the attractiveness-driven model robustly exhibits a power-law distribution, $P(n) \propto n^{-2.5}$, with an exponent independent of density. These findings, obtained through computationally intensive simulations due to long equilibration times, offer a thorough quantitative characterization of this model, highlighting the critical role of individual attractiveness in shaping social aggregation in physical space.