The way to uncover community structure with core and diversity

Communities are ubiquitous in nature and society. Individuals that share common properties often self-organize to form communities. Avoiding the shortages of computation complexity, pre-given information and unstable results in different run, in this paper, we propose a simple and effcient method to deepen our understanding of the emergence and diversity of communities in complex systems. By introducing the rational random selection, our method reveals the hidden deterministic and normal diverse community states of community structure. To demonstrate this method, we test it with real-world systems. The results show that our method could not only detect community structure with high sensitivity and reliability, but also provide instructional information about the hidden deterministic community world and our normal diverse community world by giving out the core-community, the real-community, the tide and the diversity. This is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in complex systems.