It is well known that social networks are composed of many communities of nodes, where the nodes of the same community are highly connected, and few links are between the nodes of different communities. We observe scenarios in both real-world networks as well as computer networks that opinions of nodes in the networks can be aware of the existence of communities and take them into account during opinion formation. Based on the observations, we propose the first community-aware opinion dynamics model called Sznajd~2 by applying the famous Sznajd model on the inter-community level and intra-community level. We then briefly introduce coupled fully connected networks (CFCN), analyze our model theoretically on it, and reveal that when interconnectivity parameter v > 0.172, nodes in the networks are surely to reach consensus on opinions along time, and when v < 0.172 the system might reach consensus or stay in an asymmetric stable state where some nodes disagree with others, and the state can be predicted precisely by theoretical analysis, whose correctness is also verified by simulations. For consensus performance comparison, we also perform simulations by applying our model and existing representative community-unaware models on CFCN. Simulations show that our model outperforms them, to ensure consensus on CFCN, other models require v > 0.31 at least, which is nearly two times big than our model.
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