Social Balance on Networks: Local Minima and Best Edge Dynamics

TL;DR

This paper investigates the energy landscape of social balance in signed networks, revealing local minima that trap dynamics, and introduces Best Edge Dynamics, a new process that guarantees reaching social balance efficiently.

Contribution

It introduces Best Edge Dynamics, a novel stochastic process that always converges to social balance and is proven to do so rapidly in various scenarios.

Findings

Local minima can trap social dynamics, preventing convergence.

Some local minima are robust and cannot be escaped by small perturbations.

Best Edge Dynamics guarantees reaching social balance quickly.

Abstract

Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic dynamics drives the network towards a state of minimum energy that captures social balance. It is known that this energy landscape has local minima that can trap socially-aware dynamics, preventing it from reaching balance. Here we first study the robustness and attractor properties of these local minima. We show that a stochastic process can reach them from an abundance of initial states, and that some local minima cannot be escaped by mild perturbations of the network. Motivated by these anomalies, we introduce Best Edge Dynamics (BED), a new plausible stochastic process. We prove that BED always reaches balance, and that it does so fast in various interesting settings.