The Theoretical And Applied Study On Topological Characteristics Of Complex Networks

With the quiet coming of the 21 st century,the sciences for the human race are changing with each passing day.Simple and random systems can no longer meet the requirements of rapid technological development.In order to alleviate this contradiction,the complex system as a new discipline not only indicates the direction of future development in science and technology,but also provides us with a non-linear,adaptive research approach.In the study of complex systems,the emergence of complex networks has made the complexity research outstanding in various disciplines,and resulted in discipline of network science through decades of research.Among them,the research on the topological characteristics of complex networks is the key issue,which is indispensable for improving the theory of network science and broadening its application field.In this thesis,we consider the theory and application of the topological characteristics of complex network as the research topic,and fully utilize the mathematical tools such as probability theory,calculus,and numerical analysis,and focuses on the network modeling in different environments,the solution of degree distribution and scale distribution,and the application of the average path length,etc.The main research is divided into four parts:1.An evolving scale-free networks by poisson process: modeling and degree distribution.In this thesis,in order to reveal the influence of the vertex generating mechanism of complex networks,we propose three novel models based on the homogeneous Poisson,nonhomogeneous Poisson and birth death process,respectively,which can be regarded as typical scale-free networks and utilized to simulate practical networks.The degree distribution and exponent are analyzed and explained in mathematics by different approaches.In the simulation,we display the modeling process,the degree distribution of empirical data by statistical methods,and reliability of proposed networks,results show our models follow the features of typical complex networks.2.Subnormal distribution derived from evolving networks with variable elements.in the observation of degree distributions in practical networks,we discover that,there exists a peak at the beginning of most real distributions,which cannot be accurately described by a monotonic decreasing power-law distribution.To better describe the real distributions,in this thesis,we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time.By utilizing this distribution,we can precisely describe those distributions commonly existing in the real world,e.g.,distributions of degree in social networks and personal wealth.Additionally,we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution,resulting in a better performance of fitness.3.Evolving networks based on birth and death process regarding the scale stationarity.To address this issue that the scale of network keeps growing over time without decreasing leading to the non-stationarity of the scale,in this thesis,we introduce both increasing and decreasing of vertices to build the evolving network models based on birth and death random processes which are regarded as the queueing system in mathematical.Besides the modeling,the scale of networks based on different random processes is also deduced to be stationary and denoted by a specific probabilistic expression irrelevant to time.In the simulations,we build our network models by different types of queueing systems and compare the statistical results with theories to show the validity and accuracy of our proposed models.Additionally,our model is applied to simulate and predict the populations of some developed countries in recent years.4.Highest degree likelihood search algorithm using a state transition matrix for complex networks.In order to fast travel,a novel search algorithm which employs a highest degree likelihood approach with k hunters looking for the target simultaneously is presented for different types of complex networks.A state transition matrix is applied to explain this proposed method.We compare the proposed algorithm with the methods of forerunner in the simulation,and the results show that our algorithm performs more effectively.Finally,some applications and future challenges are discussed.