Evolving Models Of Complex Networks

Complex networks have seen much interest from all research circles and have found many potential applications in a variety of fields including engineering technology, society, politics, communications, medicine, neural networks, economics and management. For example, in management domain, they have been applied to such aspects as system structure analysis, advertising, price formation, opinion formation, knowledge acquisition, information (knowledge) propagation and exchange in or between organizations. Yet despite the importance and pervasiveness of networks, scientists have had little understanding of their structure and properties. It is known to us all, randomness is in line with the major features of real-life networks, while deterministicness makes it harder to gain a visual understanding of how networks are shaped, and how do different nodes relate to each other. Therefore, it would be not only of major theoretical interest but also of great practical significance to construct models that lead to small-world networks and scale-free networks in stochastic and deterministic fashions. Especially, evolving models can not only capture correctly the processes that assembled the networks that we see today, but also help to know how various microscopic processes influence the network topology. In this paper, from both random and deterministic perspectives, evolving network models are constructed, which have the same major topologies as real-life systems.1. Two small-world network models are proposed. First, a deterministic small-world network (DSWN) model is presented by edge iterations, which is extended to an evolving small-world network (ESWN) model by including a parameter. DSWN is a special case of ESWN. In both models, when a new node is added to the network, it is only connected to those preexisting nodes that are geographically close to it. Both analytical and numerical results are obtained for relevant parameters of the two networks. The two models exhibit the classical characteristics of small-world networks: an exponential degree distribution, high clustering coefficient and a short diameter or average path length. Both the models can mimic a variety of real-life networks whose topologies are influenced by geographical constraints.2. An evolving model equivalent to the BA network and an extended BA network model are presented, respectively. The progress of preferential attachment in BA model makes it inconvenient for researcher, because it spends much time to generate networks with large order. To overcome this deficiency, first, an evolving model equivalent to BA network is proposed. The degree distribution, clustering coefficient and average path length of the evolving model are calculated analytically and simulated, which are identical to the BA network. In the evolution process of equivalent model, the global knowledge of the node degrees and preferential attachment are not necessary, this make the creation time of networks...