Tripartite and Sign Consensus for Clustering Balanced Social Networks

TL;DR

This paper introduces modified DeGroot algorithms to achieve tripartite and sign consensus in multi-agent systems with signed social networks, enabling agents to reach agreement on decisions or opinions within three clusters.

Contribution

It presents novel modifications to DeGroot's algorithm that enable tripartite and sign consensus in complex signed social networks.

Findings

Modified algorithms successfully achieve tripartite consensus.

Agents' opinions converge within three clusters.

The approach applies to networks with cooperative and antagonistic relationships.

Abstract

In this paper, we address two forms of consensus for multi-agent systems with undirected, signed, weighted, and connected communication graphs, under the assumption that the agents can be partitioned into three clusters, representing the decision classes on a given specific topic, for instance, the in favour, abstained and opponent agents. We will show that under some assumptions on the cooperative/antagonistic relationships among the agents, simple modifications of DeGroot's algorithm allow to achieve tripartite consensus(if the opinions of agents belonging to the same class all converge to the same decision) or sign consensus (if the opinions of the agents in the three clusters converge to positive, zero and negative values, respectively).