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PAGE PAGE 1泰兆基金资助课题期 末 论 文 98级物理系 程翔PAGE \# Page: # PAGE \# Page: # Department of Physics, Xiang ChengAbstractWe study a characteristic parameter of the well-known scale-free network and demonstrate that the model fails to fit the real data for its assumption that the network is symmetrical. We introduce a simple model of evolving network with inhomogeneous vertices and directional links that can best describe the real asymmetrical network. The structure of this new network is investigated with numerical and analytical approach, which shows the feature of the structure of the asymmetrical network and indicates that the network is asymptotic independent to its size. Recent discovery that many real networks such as the World-Wide Web are hierarchically organized [1,2] has brought lots of studies on the growing scale-free network with the preferential attachment [3-9]. However, this symmetrical scale-free network is incomplete when compared with real networks. Many biological, economic and communication networks are asymmetrical networks: the vertices in networks can be different and the links in networks can be directional. For instance, in the biochemical network controlling the cell division in mammals, there is great number of different substrates and enzymes that cannot be described as just one kind of vertex and the interactions between different proteins are directional: one kind of protein can contributes a peptide that binds to a receptor site or pocket on the other protein but the latter does not always has the same affect on the former [10]. Another example is the WWW whose vertices are HTML documents connected by links pointing from one page to another. The link from one HTML document to another does not assure that there is also a link pointing back from the latter document to the former [11]. One can check the data of the WWW [12], which indicates that most of the links in the WWW is unidirectional rat