2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21804We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a feedback loop which results in a first-order phase transition between a very sparse network regime and a highly-connected phase. Phase coexistence and hysteresis take place for intermediate value of parameters. We derive a mean-field theory which correctly reproduces this behavior, including the distribution of degree connectivity and the non-trivial clustering properties.5 pages 2 figuresStatistical MechanicsDisordered Systems and Neural Networkstext