  This article formalizes the problem of modeling social networks into an
interacting particle system on random geometric graphs. Each vertex of the
graph is associated with a geometric position in a latent space describing the
unobserved affinity between the network members and characterizes the strength
of the interaction between them. We endow the system with two recruitment
mechanisms that depend on the positions of the particles in the latent space
and one departure mechanism independent of the latent position. We characterize
each spatial position by a Dirac measure and the system state by a
measure-valued process which is the sum of all Dirac masses. Therefore, we
investigate the large-scale behavior of the system. In particular, using a
renormalization technique, we study the system's behavior when the initial
number of particles goes to infinity. We thus show the weak convergence of the
rescaled measure-valued process towards the solution of a deterministic
integrodifferential equation. Finally, we present some Monte Carlo simulations
with different parameter sets to illustrate the merit of our approach in
modeling some phenomena encountered in real-world networks.
