# Dynamical and Topological Aspects of Consensus Formation in Complex Networks

## TL;DR

This paper investigates how network topology and interaction rules influence consensus formation among agents navigating complex networks, highlighting the importance of non-linear interactions and degree distribution in achieving consensus.

## Contribution

It introduces an analysis of consensus dynamics on networks considering agent movement and interaction rules, emphasizing the role of non-linearity and degree distribution.

## Key findings

- Non-linear interaction rules are necessary for consensus.
- Narrower degree distributions facilitate consensus.
- Network topology significantly affects consensus emergence.

## Abstract

The present work analyses a particular scenario of consensus formation, where the individuals navigate across an underlying network defining the topology of the walks. The consensus, associated to a given opinion coded as a simple messages, is generated by interactions during the agent's walk and manifest itself in the collapse of the various opinions into a single one. We analyze how the topology of the underlying networks and the rules of interaction between the agents promote or inhibit the emergence of this consensus. We find that non-linear interaction rules are required to form consensus and that consensus is more easily achieved in networks whose degree distribution is narrower.