Topological aspects of the multi-language phases of the Naming Game on community-based networks

TL;DR

This paper investigates the topological origins of multi-language phases in the Naming Game on community networks, providing theoretical insights into phase transitions and supporting community detection applications.

Contribution

It offers a theoretical analysis of multi-language phase emergence in the Naming Game, linking metastable states to network topology and critical thresholds.

Findings

Metastable multi-language states correspond to genuine phases in the thermodynamic limit.

Critical thresholds for phase transitions depend on network topology and community structure.

Results justify using the Naming Game for community detection in networks.

Abstract

The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents converge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also examine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm.