本文關(guān)鍵詞： 復(fù)雜網(wǎng)絡(luò) 結(jié)構(gòu)特性 香農(nóng)熵 非廣延熵　出處：《西南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來,人類文明的高速發(fā)展誕生了許許多多的巨型復(fù)雜系統(tǒng),例如萬維網(wǎng),超大規(guī)模的線上社交網(wǎng)絡(luò),城市供變電系統(tǒng)以及交通運輸系統(tǒng)等,于此同時人類科學(xué)的進步也使多很以前并不了解的復(fù)雜系統(tǒng)能夠用不同的形式進行描述,例如生態(tài)網(wǎng)絡(luò),蛋白質(zhì)的相互作用網(wǎng)絡(luò),基因與蛋白的關(guān)系網(wǎng)絡(luò)等。不管是萬維網(wǎng)等人工復(fù)雜系統(tǒng)還是新發(fā)現(xiàn)的需要進行系統(tǒng)性描述的新系統(tǒng),都共有的特性是系統(tǒng)規(guī)模極大,組成系統(tǒng)的單元之間的關(guān)系復(fù)雜,關(guān)系種類繁多。我們必須去了解這些超大規(guī)模的系統(tǒng),用我們的方法去描述它們,盡可能的去維護這些巨型系統(tǒng)的穩(wěn)定健康的運行,關(guān)鍵的時候甚至需要去控制這些系統(tǒng)的運行狀態(tài)。迫切的現(xiàn)實需求和巨大的社會效益促成了復(fù)雜網(wǎng)絡(luò)這門新的學(xué)科的誕生。復(fù)雜網(wǎng)絡(luò)的研究是一門多學(xué)科交叉的研究領(lǐng)域,針對復(fù)雜網(wǎng)絡(luò)的研究為很多不同的領(lǐng)域引入了新的研究方法,與此同時對這些復(fù)雜系統(tǒng)的研究也加深了人們對復(fù)雜網(wǎng)絡(luò)模型的認識。在復(fù)雜網(wǎng)絡(luò)的研究中,復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性的評估是最重要的研究方向之一。結(jié)構(gòu)是復(fù)雜網(wǎng)絡(luò)之所以復(fù)雜的原因,結(jié)構(gòu)特性的評估是其他復(fù)雜網(wǎng)絡(luò)研究的基礎(chǔ),是復(fù)雜網(wǎng)絡(luò)在其他學(xué)科領(lǐng)域開展應(yīng)用的前提條件。因此復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu)特性的研究不僅影響復(fù)雜網(wǎng)絡(luò)的整體研究更影響著復(fù)雜網(wǎng)絡(luò)在其他各個學(xué)科中的實踐應(yīng)用。在復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性研究中,網(wǎng)絡(luò)的節(jié)點的重要度評估、網(wǎng)絡(luò)的節(jié)點的相似度度量以及網(wǎng)絡(luò)結(jié)構(gòu)復(fù)雜度的度量是最為基礎(chǔ)也是最為重要的方向。怎樣評估節(jié)點的重要度對復(fù)雜網(wǎng)絡(luò)的脆弱性與魯棒性等研究有著重要的意義,怎樣度量網(wǎng)絡(luò)中節(jié)點的相似度對網(wǎng)絡(luò)中的社團結(jié)構(gòu)探測,鏈路預(yù)測等有著重要的意義,度量網(wǎng)絡(luò)結(jié)構(gòu)的復(fù)雜度則是為了回答“復(fù)雜網(wǎng)絡(luò)到底有多復(fù)雜”這個問題,而針對復(fù)雜網(wǎng)絡(luò)的分形和自相似的研究在一定程度上是為了回答了復(fù)雜網(wǎng)絡(luò)為什么復(fù)雜的問題。在過去的研究中,許多學(xué)者提出很多的經(jīng)典方法用以對復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性進行研究,為現(xiàn)有的復(fù)雜網(wǎng)絡(luò)研究打下了堅實的基礎(chǔ)。本文將已有的經(jīng)典算法與熵這個物理概念進行了融合,從而提出基于熵的復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性評估的新的方法。本文基于熵的概念提出了四種方法用以評估復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性:一,基于局域熵的復(fù)雜網(wǎng)絡(luò)節(jié)點重要度評估方法。二,基于相對熵的復(fù)雜網(wǎng)絡(luò)節(jié)點相似度評估方法。三,基于非廣延熵的復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu)熵。四,基于非廣延熵的復(fù)雜網(wǎng)絡(luò)非廣延信息維數(shù)。熵是統(tǒng)計力學(xué)和信息論中的重要概念,將熵的概念用于復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性評估中來是本文的主要出發(fā)點。無論是信息熵還是熱力學(xué)熵,它們都是從系統(tǒng)的組成出發(fā)對系統(tǒng)的宏觀特性進行評估。本文借助熵的簡潔定義,提出了一系列簡單有效的方法用于對復(fù)雜網(wǎng)絡(luò)的結(jié)構(gòu)特性進行研究。
[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.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5

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本文編號：1547824