Vulnerability and resilience of social engagement: Equilibrium theory

¹ CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences Beijing 100190, China
² Institute of Theoretical Physics, Dalian University of Technology - Dalian 116024, China
³ School of Physical Sciences, University of Chinese Academy of Sciences - Beijing 100049, China
⁴ Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University Changsha 410081, China

^(b) luancheng@dlut.edu.cn (corresponding author)
^(c) zhouhj@itp.ac.cn (corresponding author)

Received: 30 June 2020
Accepted: 17 November 2020

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 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.