Simulation And Application Researches On Complex Networks Modeling

Recently, theoretical and empirical studies of complex networks have provided an important way to reveal the complexity of complex systems. In theoretical study, direct and visual modeling to complex networks with real system characters plays an important role, it can find the construction process of complex networks and mutual relation of nodes deeply, and catch the micro-mechanism and the dynamic characters in network evolution. In empirical study, theoretical models with itself characters and practical analysis of inner dynamics characters for real systems with different requirements are very important to reveal the construction and evolution of real system networks, and to improve the application ability in corresponding to real system requirements. In the thesis, we make research on theoretical and practical studies on complex networks modeling and application. In complex networks modeling studies, firstly, we set up the small world network and scale free network with different algorithms from the randomness and determinacy in real systems based on graph theory, and then analyze the characters of network models by computing the topology characters. In complex networks application studies, taking brain memory functional network and bus transport network for example, firstly, we model the memory network and bus transport network, and then analyze the topology characters and practice the model by the experimental data, at last we apply the complex network to the real systems with different requirements. The main contents of the thesis are as follows.1. To small world network, we set up a small world network model by the triangle inter and outer iteration algorithm with the deterministic method. By the analysis of the main topology characters, the model had small Average Path Length (APL) and big clustering coefficient. Meanwhile, it had the character of random network from the degree distribution with exponential distribution. To scale free network, we set up an extended scale free network model by the optimization algorithm. In the algorithm we introduced competition mechanism and anti-preferential mechanism based on network growth and preferential attachment. By the analysis of degree distribution, the power law index was bigger than1. With the index from1to2was the character of sub-scale free, and from2to3was the character of scale free. It was only a theoretical value with the index bigger than3. The results of the extended model implied that it was more universal corresponding to real systems.2. We set up a bi-modular model of brain memory functional network by deterministic method, in the process, the inter-modular and intra-modular nodes were abstracted by the neuron and brain cortical with the meta-memory definition, the construction and retrieve algorithms were put forward on the view of information process of memory. By the topology characters analysis, the bi-modular memory network had small APL and big clustering coefficient that was the characters of small world. The numerical simulation supported the results.3. We set up bus station network, bus transfer network and bus line network with the node abstraction from bus station and bus line, and then analyzed the dynamics topology characters of them. Because of the differences of results in different models and between real system and models, We put forward the optimization methods by getting rid of network noise and setting up virtual nodes, and then applied it to static complex network with patient medical seeking, the results satisfied the requirement of path selection. At last, by the dynamic generating algorithm the dynamic travel network was changed to static complex network and satisfied the application requirement of dynamic path selection.