Stationary States of a Random Copying Mechanism over a Complex Networks

TL;DR

This paper analyzes how agents randomly copying states in a network reach a stationary distribution independent of their degree, revealing the influence of network topology on this process.

Contribution

It introduces an analytical approach to study network dynamics, highlighting the role of influence and degree independence in stationary states across different network types.

Findings

Stationary state distribution is degree-independent.

Degree averaged means remain constant over time.

Network topology influences the influence measure.

Abstract

An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network topology on the process are characterized introducing a quantity called influence and studying its behavior for scale-free and random networks. We show that for this model degree averaged means are constant in time regardless of the number of states involved.