Vulnerability and Resilience of Social Engagement: Equilibrium Theory

Social networks of engagement sometimes dramatically collapse. A widely adopted paradigm to understand this catastrophe dynamics is the threshold model but previous work only considered the irreversible K-core pruning process and the resulting kinetic activity patterns. Here we study the network alliance problem as a simplified model of social engagement by equilibrium statistical mechanics. Our theory reveals that the surviving kinetic alliances are out-of-equilibrium and atypical configurations which may become highly vulnerable to single-node-triggered cascading failures as they relax towards equilibrium. Our theory predicts that if the fraction of active nodes is beyond a certain critical value, the equilibrium (typical) alliance configurations could be protected from cascading failures by a simple least-effort local intervention strategy. We confirm these results by extensive Monte Carlo simulations.