  It is interesting and of significant importance to investigate how network
structures co-evolve with opinions. The existing models of such co-evolution
typically lead to the final states where network nodes either reach a global
consensus or break into separated communities, each of which holding its own
community consensus. Such results, however, can hardly explain the richness of
real-life observations that opinions are always diversified with no global or
even community consensus, and people seldom, if not never, totally cut off
themselves from dissenters. In this article, we show that, a simple model
integrating consensus formation, link rewiring and opinion change allows
complex system dynamics to emerge, driving the system into a dynamic
equilibrium with co-existence of diversified opinions. Specifically, similar
opinion holders may form into communities yet with no strict community
consensus; and rather than being separated into disconnected communities,
different communities remain to be interconnected by non-trivial proportion of
inter-community links. More importantly, we show that the complex dynamics may
lead to different numbers of communities at steady state with a given tolerance
between different opinion holders. We construct a framework for theoretically
analyzing the co-evolution process. Theoretical analysis and extensive
simulation results reveal some useful insights into the complex co-evolution
process, including the formation of dynamic equilibrium, the phase transition
between different steady states with different numbers of communities, and the
dynamics between opinion distribution and network modularity, etc.
