小世界理论在复杂网络中的研究与应用
发布时间：2018-08-30 14:28
【摘要】：小世界理论作为研究复杂网络的一个基本理论,展现了复杂网络的高聚类系数与低平均距离的特性。其最初由社会学家提出,研究的对象为社会网络的构成、交互、演变以及对于人类社会的影响。随着现代科技的发展,小世界理论逐渐成为了研究网络结构、演变与性质的一种重要研究方法和手段。在拓扑学、社会科学、信息科学、病毒传播学都已经发挥了重要作用之后,小世界理论在金融学、公共安全、管理学、电子学等领域的重要性逐渐显现。本论文主要针对具有小世界特性的复杂网络进行研究,分析网络的信息流。首先,研究信息流的传递。针对经典的WS模型进行修改,将模型改为更贴近实际的网格模型,提出网格模型中的邻边(短边)与长边的概念。因人际网络中人际能量的有限性,分配网格节点有限连接边,证明此网络具有小世界性。为动态展现网络中信息传递的迅速性,提出三权值云熵层次分析法小世界路径选择模型,将节点间距离、节点度、节点密集度作为主要考虑因素,运用层次分析法分析,并用云熵模型赋予节点一定的选择自由度。算法的仿真结果证明,此算法可以在通过较短中间节点连接网络中的任意两个节点。然后,研究信息流的抑制。针对病毒传播在具有小世界特性的复杂网络进行了研究。网络中病毒传播拥有较大的动态性,所以采用了元胞自动机进行模拟。赋予网络中节点断开与重连的自适应性,使节点可以自行避开高危节点。引入危害认识函数,使节点的断开与重连率与危害认识展现一定相关性。用全局预警的方式影响危害认识函数,使节点拥有宏观认识下,处理自身(微观)的连接。运用仿真得到具有小世界特性的复杂网络上病毒传播的一些特性,并说明全局预警对于病毒传播的抑制作用。
[Abstract]:As a basic theory of studying complex networks, small-world theory shows the characteristics of high clustering coefficient and low average distance of complex networks. It was originally proposed by sociologists to study the composition, interaction, evolution of social networks and their impact on human society. In order to study the network structure, evolution and nature of an important research method and means. In topology, social sciences, information science, viral communication have played an important role, the small world theory in finance, public security, management, electronics and other fields of importance gradually emerged. This paper focuses on the small world. Firstly, the transmission of information flow is studied. The classical WS model is modified to a more realistic grid model. The concepts of adjacent edges (short edges) and long edges in the grid model are proposed. In order to show the rapidity of information transmission in the network dynamically, a three-weight cloud entropy analytic hierarchy process (TWCAHP) model for small-world path selection was proposed. The distance between nodes, degree of nodes and degree of node density were considered as the main factors, and the analytic hierarchy process (AHP) was used to analyze the network and the cloud entropy model was used to give the nodes certain selection. The simulation results show that the algorithm can connect any two nodes in the network through a shorter intermediate node. Then, the suppression of information flow is studied. It gives the nodes in the network the self-adaptability of disconnection and reconnection, so that the nodes can avoid high-risk nodes by themselves. Introduce the hazard recognition function, so that the disconnection and reconnection rate of the nodes and hazard awareness show a certain correlation. Some characteristics of virus propagation on complex networks with small-world characteristics are obtained by simulation, and the inhibition effect of global early warning on virus propagation is illustrated.
【学位授予单位】：辽宁科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5
本文编号：2213350
[Abstract]:As a basic theory of studying complex networks, small-world theory shows the characteristics of high clustering coefficient and low average distance of complex networks. It was originally proposed by sociologists to study the composition, interaction, evolution of social networks and their impact on human society. In order to study the network structure, evolution and nature of an important research method and means. In topology, social sciences, information science, viral communication have played an important role, the small world theory in finance, public security, management, electronics and other fields of importance gradually emerged. This paper focuses on the small world. Firstly, the transmission of information flow is studied. The classical WS model is modified to a more realistic grid model. The concepts of adjacent edges (short edges) and long edges in the grid model are proposed. In order to show the rapidity of information transmission in the network dynamically, a three-weight cloud entropy analytic hierarchy process (TWCAHP) model for small-world path selection was proposed. The distance between nodes, degree of nodes and degree of node density were considered as the main factors, and the analytic hierarchy process (AHP) was used to analyze the network and the cloud entropy model was used to give the nodes certain selection. The simulation results show that the algorithm can connect any two nodes in the network through a shorter intermediate node. Then, the suppression of information flow is studied. It gives the nodes in the network the self-adaptability of disconnection and reconnection, so that the nodes can avoid high-risk nodes by themselves. Introduce the hazard recognition function, so that the disconnection and reconnection rate of the nodes and hazard awareness show a certain correlation. Some characteristics of virus propagation on complex networks with small-world characteristics are obtained by simulation, and the inhibition effect of global early warning on virus propagation is illustrated.
【学位授予单位】：辽宁科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5
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