Research On The Topological Structures Of Complex Networks

New advances in many fields, ranging from communications, computer science to biology, are hindered by the limited understanding of the complex systems, and the complexity of many systems in nature and society can be attributed to the complexity of interwoven webs like Internet and ecological web through which the systems'constituents interact linearly or nonlinearly with each other, then emerges the research for complex networks. As a branch of complexity science, the research for complex networks has drawn more and more attentions among scholars, and progresses have been made both theoretically and practically. This paper aims at the research on topological structures of complex networks which is the base for the research on the dynamic properties of complex networks. In this paper, the research background and development for complexity science and complex networks are introduced, then several important topological parameters of complex networks are investigated at length, and several important complex network models are analyzed in detail. Lastly the influence of network topological structures on the error and attack tolerance characteristics of complex networks is presented briefly. The main research work is as follows:1)The topological structures of the Internet at AS level are studied. The concept of connection rate is defined, and a new power law relation that the connection rates of ASs obeyed is found, which demonstrates empirically that there is an AS core in the Internet that is constituted by few ASs with large degrees and strong connectivity among them.2)To characterize heterogeneity of general complex networks quantificationally, the concept of Gini coefficient in Microeconomics is borrowed. The Gini coefficient is the first concept used to characterize heterogeneity of general complex networks quantificationally with uniform criterion. Moreover the use of the Gini coefficient can classify infinite scale-free networks as only two categories strictly and may explain why the degree exponents of most real-world scale-free networks are larger than two from a new perspective.3) For the first time the topological structure of China Railway Network (CRN) is investigated roundly, and some important topological parameters on CRN, like cumulative degree distribution, cumulative probability distribution of the number of trains, cumulative probability distribution of the number of stations, cluster coefficient and path lengths, are obtained, and small world property of it is found. Furthermore someother important parameters on CRN like network efficiency are obtained, and all these results are with potential theoretical value and practical significance for the construction and optimization of CRN.