Coexistence of balance and hierarchies: An ego perspective to explain empirical networks.

Abstract

The formation of positive and negative relations between individuals in social networks can be described by different approaches. Two prominent mechanisms are structural balance and status hierarchies. Balance motivates stability among friends and enemies in triads (e.g. an enemy of my friend is my enemy). Status considers respect and disregard originating from social hierarchy (e.g. positive relations towards those we respect). We demonstrate that integrating the two mechanisms through the concept of ego dynamics is key to understanding observable patterns in many social groups. We propose an agent-based model where dynamical changes result from agents aiming to resolve inconsistencies with structural balance and status. In contrast to previous models, our approach employs the ego perspective. Agents have limited, local knowledge and can only change their own relations. By fitting the model to real-world networks, we successfully replicated the observed over- and under-representations of certain triads in 36 empirical signed networks. This close matching to empirical data is achievable only by taking the ego perspective and not assuming global knowledge. Additionally, the model reveals that, when the status mechanism dominates, people in real networks tend to strive for the top of the hierarchy. Finally, our numerical simulations and analytic solutions demonstrate that a previously thought as continuous phase transition towards the paradise state (all links positive) can become discontinuous when the status mechanism is involved. This discontinuity indicates that desirable social configurations may, in fact, be quite fragile.