ZHANG Si-Ying
In this paper the concept of ``self-clustering" is presented. It is one kind of the self-organizing and widely existing in complex systems. For the function of complex systems, there is a well-known inequality $1+1>2$ , showing that the whole is more than the sum of its parts. Could it seek one more quantitative expression for the function of complex systems? For this purpose a simple but widely representative network model is given. With this model, the process of growing, evolving and emergence of the system can be analyzed and a quantitative/qualitative expression $f(n)=\frac{1}{2}n(n-1)$ for system function can be derived. This expression indicates properties of the system function and gives explanations of some important phenomena. Such as: $1+1>2$ is a special case of $f(n)$ as $n=2$. Moreover, $f(n)$ shows the nonlinearity obviously. It also shows that at the initial stage of the process, adding or losing a few components will give rise to notable effect to the system function. There will be a steady emergence as $n$ increased to a considerable amount.
Thus, it reveals the change that from the fragility at the initial stage to the robustness accompanying the steady emergence. In addition, $f(n)$ implies positive feedback. An expression is given to show this mechanism, which turns out to be the mechanism of "increasing returns" and the mechanism of ``preferential attachment", leading to the scale-free network structure. Finally, a brief conclusion regarding complexity and simplicity is given.