On the role of volatility in the evolution of social networks

TL;DR

This paper investigates how different types of volatility influence the evolution of social networks, revealing phase transitions between ordered and disordered states depending on whether volatility affects links or nodes.

Contribution

It introduces a simple model demonstrating how link- and node-based volatility lead to distinct network phases and identifies a unique second order phase transition.

Findings

Link volatility causes a sharp transition between dense and sparse networks.

Node volatility results in only a disordered, sparse network phase.

The phase transition exhibits an unusual critical exponent of zero.

Abstract

We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition between order -- promoted by the efforts of agents to coordinate -- and disorder induced by volatility in the underlying social network. We find that when volatility affects mostly the decay of links, the model exhibit a sharp transition between an ordered phase with a dense network and a disordered phase with a sparse network. When volatility is mostly node-based, instead, only the symmetric (disordered) phase exists These two regimes are separated by a second order phase transition of unusual type, characterized by an order parameter critical exponent $\beta=0^+$. We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction.