Evolving Network Models Under A New Growing Mechanism

The study of complex networks plays a key role in theunderstanding of the structures and behaviors of complex systems,thus it has recently become one of the most promising researchsubjects in the scientific community. In 1999, Barabási and Albert(BA) found that many real-world networks exhibit the scale-freeproperty. Since then, the exploration of the correspondingmicroscopic mechanisms leading to the macroscopic properties ofreal systems, as well as the investigation of the law of networkevolution, etc, has become the focus of attention in this field. In thisthesis, we propose a new mechanism of network growth whichincludes the adding and deletion of nodes, and explore systematicallythe macroscopic properties of evolving network models under thismechanism. This study is believed to be able to shed some light onthe formation and evolution of complex network systems. The thesis consists of five chapters. In chapter one, we give a briefreview to the history of network study. Then we introduce briefly theproperties of two kinds of important static network models, i.e., theER model and the small-world model. In chapter two, we introducebriefly the properties of two kinds of evolving network models: therandom evolving network model and the BA model. In chapter three,based on careful examination of experimental data from lots ofexisting papers, we propose to divide the fat-tailed degreedistributions of real-world networks into five classes. Then wepropose a new growing mechanism which includes the adding anddeletion of nodes. When the probabilities of adding and deletion ofnodes in the mechanism are treated as constants (simple ADmechanism), we obtain all the five classes of degree distributions ofreal systems in evolving network models under the simple ADmechanism. In chapter four, based on the simple AD mechanism, weintroduce the Logistic dynamic equation into the network evolution.And the probabilities of adding and deletion of nodes in the growingmechanism are described by such equation (Logistic AD mechanism).In the evolving network models under the Logistic AD mechanism,we obtain all the five classes of degree distributions of real systems.In addition, we find that the degree distribution of networks evolveswith time. The chapter five presents a conclusion for our work andsome prospects for future works in this field.