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

On the basis of several new concepts, such as, the relationship flow and the basic level of a network, and by applying the Structural Theory of General Systems, this article conducts a study of the relationships and their laws between the relationship flows, including information flows, matter flows, energy flows, fund flows, personnel flows, and so on, and the behavior or function of a network, and mathematically obtains two theorems, namely the network's relationship flow-behavior theorem 1 and 2. It then proposes a new model of networks, called the relationship flow-behavior model of networks, which shows that for a network, its behavior or function is determined and governed only by its input flow Rf(t) and relationship flow set Rfnb(t) on its so-called basic level Hb, that is, its total relationship flows TRf(t)= Rf(t) ∪ Rfnb(t), especially by the relationship flow cycle(s) in TRf(t). By a further mathematical study of the model, it can be expected to obtain a series of inherent relationships and their laws between the relationship flows and the behavior or function of a network, as well as their derivates, for example, the issues, ideas, theories, methods, approaches, and tools of network research, which would make significant contributions to the advancement of network research.