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

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 reach global consensus on naming an object asymptotically through iterative pair-wise conversations. The underlying communication network indicates the relationships among the individuals. In this paper, three typical topologies of human communication networks, 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) when the intra-community connections increase while the inter-community connections remain to be unchanged, the convergence to global consensus is slow and eventually might fail; 2) when the inter-community connections are sufficiently dense, both the number and the size of the communities do not affect 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.