Eur. Phys. J. B 65, 595-600 (2008)
https://doi.org/10.1140/epjb/e2008-00365-8

On the role of volatility in the evolution of social networks

¹ International school for advanced studies SISSA and INFN, via Beirut 2-4, 34014 Trieste, Italy
² The Abdus Salam ICTP, Strada costiera 11, 34014 Trieste, Italy

Corresponding author: ^a ddemarti@sissa.it

Received: 2 July 2008
Revised: 1 September 2008
Published online: 25 September 2008

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 β = 0⁺. We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction.