Generalized Cooperation Network

The dynamics principles, which describe the actors'behaviors in complex self-adaptive systems, should include some characters similar to what are shown by the living systems, such as forecasting, choice, learning, and evolution. Each actor and his behavior are different. Also, a system consisting of actors is not a simple combination of them. It cannot be treated by reduction theory, and cannot be described by the conventional mathematics, which serve for determinism and reductionism. We must develop some new methods and tools to describe self-adaptive systems. The latest development in the complex network gives us a possible way for searching the possibility.The complex network can describe variety different practical systems. We have carried out empirical studies on quite some practical systems; wish to classify the systems based on the results and find out the common statistical properties of every kind of them. The next step could be setting up suitable models so that we could understand their common dynamical characteristics and mechanism. In this way we can reach, step by step, to a more universal understanding on complex systems. Among the very wide scope of complex network studying, our interests are concentrated on the so-called"generalized collaboration networks". In such networks the nodes (actors) are participating a lot of collaborative acts. In the study we shall only consider actor's cooperation, and ignore the competition, confrontation or other type of relations between them. We propose define actor's cooperation in the acts as edges. In this way, one act can be described by a complete graph composed by the actors where every pair of them are connected with edges. Such a network may not be a social network, it can belong to many other kinds of networks too, but because the topological structure has common characteristics, their statistics properties have common characteristics. Among the practical networks we empirically studied, we found that the Chinese tourist line network, the public transportation network in Beijing and Yangzhou, the traditional Chinese medicine prescription network, and Huai-Yang recipe network can be described by the generalized collaboration networks. After the analysis on the empirical data, we have obtained some common statistical properties: First of all, the act is a leading factor in this kind of networks. The act degree distribution (the distribution of the number of the acts, in which the actors are participating) should be, very possibly, the most...