复杂网络关系流与行为关系定理——一般系统结构理论在复杂网络中的应用

The Complex Network's Relationship Flow-Behavior Theorems——The Structural Theory of General Systems Applied in Complex Network

在关系流概念的基础上,应用一般系统结构理论,研究复杂网络的关系流,包括信息流、物流、能量流、资金流、人力资源流等和复杂网络行为或功能之间的关系及规律,得到两个复杂网络关系流与行为关系定理和一个复杂网络关系流与行为关系模型.它们表明,对于任何一个复杂网络,复杂网络行为或功能仅由它的输入流Rf(t)和基层次Hd上的关系流集Rfcnd(t)——复杂网络关系流CNRf(t)=Rf(t)∪Rfcnd(t),特别是其中的关系流回路,决定和支配的.通过对复杂网络关系流与行为关系模型的数学研究,可以从理论上揭示复杂网络关系流和复杂网络行为或功能之间存在的一系列固有关系及规律,以及这些关系及规律衍生的复杂网络研究思想、理论、方法、手段和工具,推动复杂网络研究的发展.

Based on the concept of a relationship flow and applying the Structural Theory of General Systems, this paper makes the study of the relationships and their laws between the relationship flows, including information flows, matter flows, energy flows, fund flows, personnel flows, etc. ~and the behavior or function of a complex network, and mathematically obtains two theorems and a model, called the Complex Network＇s Relationship Flow-Behavior Theorem 1 and 2, and the Complex Network＇s Relationship Flow-Behavior Model CNM（1-2）, respectively, which show that for a complex network, its behavior or function is determined and governed only by its input flow Rf（t） and relationship flow set Rfcnd （t） at the so-called basic level H4 of its hierarchy, i.e. its total relationship flows CNRf（ t ） = Rf（ t ） U Rfcnd （ t ）, especially by the relationship flow cycles in CNRf（ t ）. By the further mathematical study of the model, we can obtain a series of the inherent relationships and their laws between the relationship flows and the behavior or function of a complex network, as well as their derivates, e.g. the ideas, theories, methods, approaches and tools of a complex network, etc. which would make significant contributions to the advancement of complex network research.