【作者】 张兰华；

【导师】 唐一源；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2013， 博士

【摘要】 近年来,复杂网络的理论和实证研究,对于揭示复杂系统的复杂性提供了一个重要的手段。在理论研究中,结合真实系统的性质形象直观的进行复杂网络建模,对于深入了解复杂网络的形成过程和不同节点间的相互关系,捕捉网络演化微观机制和动态特性具有重要的意义；在实践研究中,构造符合自身特性的理论模型以及针对不同的需求实证分析真实系统内在的动力学性质,对于揭示现实系统对应复杂网络的形成及演化机制,提高复杂网络对实际系统需求的应用能力是非常重要的。因此,本文从复杂网络建模和应用两个角度进行理论与实践研究。对于复杂网络建模,以图论为基础,结合真实系统的随机性和确定性,分别利用不同的建模算法对小世界网络和无标度网络进行建模,通过对网络拓扑属性的计算解析网络模型的特性。对于复杂网络应用,以脑记忆功能网络和公交网络为例,首先建立相应的复杂网络模型,其次解析计算网络的拓扑属性,然后利用实验数据进行模型实证分析,最后结合不同的需求进行复杂网络应用研究。主要研究内容如下：1、对于小世界网络,利用确定性建模的方式,根据三角形内外迭代算法不断增长,建立了一个小世界网络模型,解析计算主要拓扑属性发现,模型具有较短的平均路径长度和较大的聚类系数,而网络度分布服从指数分布说明网络模型同时具有随机网络的性质。对于无标度网络,在网络增长和择优连边机制的基础上,引入竞争机制和反择优删除连边机制,根据优化算法建立了一个无标度网络扩展模型,解析计算网络的度分布发现,网络的幂律指数大于1,1到2为亚标度,2到3为无标度,大于3只在理论上存在,说明模型对应更广泛的实际系统,适用性更强。2、通过确定性的方式,利用元记忆的定义抽象神经元和脑区为内模和外模节点,根据记忆的信息处理过程提出了构造算法和检索算法,建立了脑记忆功能双模结构网络,通过对网络拓扑属性的分析发现,双模记忆网络具有较短的平均路径长度和较大的聚类系数,属于小世界网络,数值模拟的结果验证了算法及模型的有效性。3、以公交站点和公交线路为节点,建立了公交站点网络、公交换乘网络和公交线路网络,通过实验数据解析计算了三种网络的动力学拓扑特性,根据模型结果的不同以及与实际系统特征表现出的不相符,利用网络去噪和建立虚拟节点的方式提出了网络优化方法,应用于患者就医静态复杂网络中,实现了路径选择的需求；最后利用动态建模算法将动态旅游网络转换为静态复杂网络,解决了旅游出行时的动态路径选择问题。更多还原

【Abstract】 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.更多还原