Dynamics of Social Balance on Networks

TL;DR

This paper investigates how social networks evolve under a dynamic process that balances friendly and unfriendly links, revealing a phase transition and conditions leading to a fully balanced state.

Contribution

It introduces a model of social balance dynamics with a phase transition and analyzes how networks reach balanced states under different constraints.

Findings

Infinite networks undergo a phase transition at p=1/2.

Finite networks always reach a balanced state.

Additional constraints accelerate the balancing process.

Abstract

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.