Local communities obstruct global consensus: Naming game on multi-local-world networks

TL;DR

This study investigates how community structures within social networks influence the convergence of the naming game, revealing that strong local communities can hinder or prevent reaching global consensus.

Contribution

The paper introduces a detailed simulation analysis of the naming game on multi-local-world networks with various topologies, highlighting the impact of community structure on consensus formation.

Findings

Stronger community structures slow down or prevent global consensus.

Dense inter-community connections facilitate consensus regardless of community size.

Local clustering within networks obstructs global consensus despite similar average degrees.

Abstract

Community structure is essential for social communications, where individuals belonging to the same community are much more actively interacting and communicating with each other than those in different communities within the human society. Naming game, on the other hand, is a social communication model that simulates the process of learning a name of an object within a community of humans, where the individuals can generally reach global consensus asymptotically through iterative pair-wise conversations. The underlying network indicates the relationships among the individuals. In this paper, three typical topologies, namely random-graph, small-world and scale-free networks, are employed, which are embedded with the multi-local-world community structure, to study the naming game. Simulations show that 1) the convergence process to global consensus is getting slower as the community structure becomes more prominent, and eventually might fail; 2) if the inter-community connections are sufficiently dense, neither the number nor the size of the communities affects the convergence process; and 3) for different topologies with the same average node-degree, local clustering of individuals obstruct or prohibit global consensus to take place. The results reveal the role of local communities in a global naming game in social network studies.