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

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