The Rise and Fall of a Networked Society

TL;DR

This paper introduces a simple model of social network evolution emphasizing local search and link volatility, revealing a phase transition between sparse and highly-connected networks with hysteresis effects.

Contribution

It presents a mean-field theory that accurately predicts network phase transitions, degree distribution, and clustering properties in a dynamic social network model.

Findings

Identifies a first-order phase transition in network connectivity.

Shows coexistence and hysteresis in network states.

Derives a mean-field theory matching simulation results.

Abstract

We 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.