Ternary Social Networks: Dynamic Balance and Self-Organized Criticality

TL;DR

This paper extends the binary social network model to ternary relations, analyzing dynamic balance, relation distributions, and self-organized criticality, revealing power-law behavior in avalanches caused by small disturbances.

Contribution

It introduces a generalized ternary social network model, studying its dynamic balance and criticality, which was not addressed in previous binary models.

Findings

Distribution of relations at dynamic balance

Time to reach dynamic balance

Power-law distribution of avalanches

Abstract

Antal et al. [Phys. Rev. E \textbf{72}, 036121 (2005)] have studied the balance dynamics on the social networks. In this paper, based on the model proposed by Antal et al., we improve it and generalize the binary social networks to the ternary social networks. When the social networks get dynamically balanced, we obtain the distributions of each relation and the time needed for dynamic balance. Besides, we study the self-organized criticality on the ternary social networks based on our model. For the ternary social networks evolving to the sensitive state, any small disturbance may result in an avalanche. The occurrence of the avalanche satisfies the power-law form both spatially and temporally. Numerical results verify our theoretical expectations.