Noise in Naming Games, partial synchronization and community detection in social networks

TL;DR

This paper introduces Noisy Naming Games, a Markov Chain model with noise, which enables community detection in social networks by analyzing states with minimal Gibbs energy that reveal hidden community structures.

Contribution

The paper develops a Markov Chain model for Naming Games with noise, linking it to Markov Random Fields to improve community detection in social networks.

Findings

Noisy Naming Games are ergodic with all partial consensus states recurrent.

Stationary distribution relates to a Markov Random Field with local specifications.

States with lowest Gibbs energy reveal hidden community structures.

Abstract

The Naming Games (NG) are agent-based models for agreement dynamics, peer pressure and herding in social networks, and protocol selection in autonomous ad-hoc sensor networks. By introducing a small noise term to the NG, the resulting Markov Chain model called Noisy Naming Games (NNG) are ergodic, in which all partial consensus states are recurrent. By using Gibbs-Markov equivalence we show how to get the NNG's stationary distribution in terms of the local specification of a related Markov Random Field (MRF). By ordering the partially-synchronized states according to their Gibbs energy, taken here to be a good measure of social tension, this method offers an enhanced method for community-detection in social interaction data. We show how the lowest Gibbs energy multi-name states separate and display the hidden community structures within a social network.