Analysis Of Evolutionary Models Of Complex Networks With Different Combinations Of Randomness And Tendencies

Complex networks can describe a large number of real systems in a highly way.Empirical studies show that the generation and evolution of real networks are both random and tendentious.The basic problems of complex network research involve the discovery of the underlying evolutionary mechanisms and the construction of evolutionary models.The analysis and study of the formation mechanisms of networks are helpful to understand the complex interactions between a large number of individual elements in nature and in human society.In order to deeply study the influences of randomness and tendencies on the properties of complex networks,the following two major types of evolutionary models are constructed based on the analysis of the classical BA(Barabasi-Albert)and ER(Erdos-Renyi)network models:1.Three evolution,ary models of growth,networks with randomness.On the basis of random networks with gradually increasing nodes,three models of growth networks are constructed by modifying the connection mechanisms:the model with the connection probability as functions of node degree,the model with the random preferential connections of local nodes,and the model with the random walk connections.Through numerical experiments,it is found that random networks can transit to scale-free networks under certain conditions.2.Four evolutionary models of random networks with tendencies.The ER net-work is an ideal model with a fixed connection probability and a Poisson distribution of degrees.However,the connection probability of real networks is not uniform and the degree distribution does not coinpletely conform to the Poisson distribution.Based on the ER networkmodel,four models of random networks with tendencies are constructed:the model with the connection probability as functions of the dif-ference between node degrees,the model with the preferential connections by the difference between node degrees,the model with random connections of neighbor nodes,and the model with the random walk connections.The influences of differ-ent tendencies on the topological structure and characteristics of random networks are analyzed.Comparing the degree distribution characteristics of the modified evolutionary models with that of the classical BA and ER models,itcan be found that there is no strict boundary between random networks and the scale-free networks.Under the conditions of different combinations of randomness and tendencies,the transitions between random networks and scale-free networks can be realized.