Vulnerability and Resilience of Social Engagement: Equilibrium Theory

TL;DR

This paper models social engagement networks using equilibrium statistical mechanics, revealing how alliances can be vulnerable to cascading failures and how simple interventions can prevent collapse.

Contribution

It introduces a new equilibrium-based model for social engagement, contrasting previous irreversible models, and predicts intervention strategies to enhance network resilience.

Findings

Surviving alliances are out-of-equilibrium configurations.

High active node fraction can prevent cascading failures.

Simple local interventions can protect network stability.

Abstract

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.