基于熵的复杂网络结构特性研究

发布时间：2018-02-28 15:09

本文关键词： 复杂网络结构特性香农熵非广延熵　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,人类文明的高速发展诞生了许许多多的巨型复杂系统,例如万维网,超大规模的线上社交网络,城市供变电系统以及交通运输系统等,于此同时人类科学的进步也使多很以前并不了解的复杂系统能够用不同的形式进行描述,例如生态网络,蛋白质的相互作用网络,基因与蛋白的关系网络等。不管是万维网等人工复杂系统还是新发现的需要进行系统性描述的新系统,都共有的特性是系统规模极大,组成系统的单元之间的关系复杂,关系种类繁多。我们必须去了解这些超大规模的系统,用我们的方法去描述它们,尽可能的去维护这些巨型系统的稳定健康的运行,关键的时候甚至需要去控制这些系统的运行状态。迫切的现实需求和巨大的社会效益促成了复杂网络这门新的学科的诞生。复杂网络的研究是一门多学科交叉的研究领域,针对复杂网络的研究为很多不同的领域引入了新的研究方法,与此同时对这些复杂系统的研究也加深了人们对复杂网络模型的认识。在复杂网络的研究中,复杂网络的结构特性的评估是最重要的研究方向之一。结构是复杂网络之所以复杂的原因,结构特性的评估是其他复杂网络研究的基础,是复杂网络在其他学科领域开展应用的前提条件。因此复杂网络结构特性的研究不仅影响复杂网络的整体研究更影响着复杂网络在其他各个学科中的实践应用。在复杂网络的结构特性研究中,网络的节点的重要度评估、网络的节点的相似度度量以及网络结构复杂度的度量是最为基础也是最为重要的方向。怎样评估节点的重要度对复杂网络的脆弱性与鲁棒性等研究有着重要的意义,怎样度量网络中节点的相似度对网络中的社团结构探测,链路预测等有着重要的意义,度量网络结构的复杂度则是为了回答“复杂网络到底有多复杂”这个问题,而针对复杂网络的分形和自相似的研究在一定程度上是为了回答了复杂网络为什么复杂的问题。在过去的研究中,许多学者提出很多的经典方法用以对复杂网络的结构特性进行研究,为现有的复杂网络研究打下了坚实的基础。本文将已有的经典算法与熵这个物理概念进行了融合,从而提出基于熵的复杂网络的结构特性评估的新的方法。本文基于熵的概念提出了四种方法用以评估复杂网络的结构特性:一,基于局域熵的复杂网络节点重要度评估方法。二,基于相对熵的复杂网络节点相似度评估方法。三,基于非广延熵的复杂网络结构熵。四,基于非广延熵的复杂网络非广延信息维数。熵是统计力学和信息论中的重要概念,将熵的概念用于复杂网络的结构特性评估中来是本文的主要出发点。无论是信息熵还是热力学熵,它们都是从系统的组成出发对系统的宏观特性进行评估。本文借助熵的简洁定义,提出了一系列简单有效的方法用于对复杂网络的结构特性进行研究。
[Abstract]:In recent years, the rapid development of human civilization has given birth to many huge and complex systems, such as the World wide Web, large-scale online social networks, urban power supply systems and transportation systems, etc. At the same time, advances in human science have enabled many previously unknown complex systems to be described in different forms, such as ecological networks, protein interaction networks, Whether it's artificial complex systems like the World wide Web or newly discovered new systems that need to be systematically described, they all share the characteristics of the scale of the system and the complexity of the relationship between the units that make up the system. There are a variety of relationships. We have to understand these very large systems, describe them in our own way, and try to maintain the stability and health of these giant systems as much as possible. Critical times even need to control the operating state of these systems. The urgent practical needs and great social benefits have contributed to the birth of the complex network, a new discipline. Complex network research is a multidisciplinary research field. The research on complex networks has introduced new research methods for many different fields. At the same time, the study of these complex systems has also deepened the understanding of complex network models. The evaluation of structural characteristics of complex networks is one of the most important research directions. Therefore, the study of complex network structure not only affects the overall study of complex network, but also affects the practical application of complex network in other disciplines. In the study of the structural characteristics of complex networks, The importance of the nodes of the network, The measurement of node similarity and the complexity of network structure are the most basic and important directions. How to evaluate the importance of nodes plays an important role in the research of vulnerability and robustness of complex networks. How to measure the similarity of nodes in the network is of great significance to the community structure detection and link prediction in the network. The complexity of the network structure is measured to answer the question of "how complex the complex network is". To some extent, the research on fractal and self-similarity of complex networks is to answer the question of why complex networks are complex. Many scholars have proposed many classical methods to study the structural characteristics of complex networks, which have laid a solid foundation for the existing research of complex networks. In this paper, the existing classical algorithms and the physical concept of entropy are fused. Based on the concept of entropy, four methods are proposed to evaluate the structural characteristics of complex networks. A method for evaluating the importance of complex network nodes based on local entropy. Second, the similarity evaluation method of complex network nodes based on relative entropy. Third, the entropy of complex network structure based on non-extensive entropy. Non-extended information dimension of complex networks based on nonextended entropy. Entropy is an important concept in statistical mechanics and information theory. The main starting point of this paper is to apply the concept of entropy to the evaluation of structural characteristics of complex networks, whether it is information entropy or thermodynamic entropy. In this paper, by virtue of the simple definition of entropy, a series of simple and effective methods are proposed to study the structural characteristics of complex networks.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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