【摘要】：自然界中,復(fù)雜網(wǎng)絡(luò)系統(tǒng)隨處可見。不管是人們可以感知的經(jīng)濟系統(tǒng)、引文網(wǎng)絡(luò)系統(tǒng)、食物鏈網(wǎng)絡(luò)系統(tǒng),還是人們不可感知的生物化學(xué)系統(tǒng),這些復(fù)雜網(wǎng)絡(luò)系統(tǒng)都擁有著各自的屬性和聯(lián)系。為了充分地研究這些復(fù)雜網(wǎng)絡(luò)系統(tǒng),學(xué)者們抽象出一種模型—復(fù)雜網(wǎng)絡(luò)。近年來,復(fù)雜網(wǎng)絡(luò)的崛起引起了相關(guān)領(lǐng)域?qū)＜覀兊母叨汝P(guān)注,也迅速成為他們研究的重點內(nèi)容。學(xué)者們通過進一步地研究和分析,發(fā)現(xiàn)不同的現(xiàn)實網(wǎng)絡(luò)模型卻有著相同的特性。社團結(jié)構(gòu)是描述復(fù)雜網(wǎng)絡(luò)的一個關(guān)鍵特征,也是網(wǎng)絡(luò)中最普通且最關(guān)鍵的一個拓?fù)鋵傩�。研究社團結(jié)構(gòu)不僅具有重要的理論意義,而且具有實際應(yīng)用價值。社團結(jié)構(gòu)可以幫助人們更好地認(rèn)識和了解網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)、復(fù)雜網(wǎng)絡(luò)的功能模塊、節(jié)點之間的隱藏關(guān)系,也可以預(yù)測網(wǎng)絡(luò)系統(tǒng)的變化趨勢。在復(fù)雜網(wǎng)絡(luò)的社團結(jié)構(gòu)識別過程中,模塊度度量和其衍生出的度量指標(biāo)起了很重要的作用,并催生了一大批重要的社團識別算法。但這種通過一般模塊度優(yōu)化方法來獲取復(fù)雜網(wǎng)絡(luò)的社團結(jié)構(gòu)存在分辨率問題,影響了模塊度優(yōu)化方法的準(zhǔn)確性和應(yīng)用廣度。針對模塊度優(yōu)化時所產(chǎn)生的分辨率問題,本文將提出應(yīng)用增強模塊度優(yōu)化方法,從而有效地避免分辨率問題。由于社團結(jié)構(gòu)的劃分和聚類算法的思想類似,可以探索使用數(shù)據(jù)挖掘的方法和理論來研究復(fù)雜網(wǎng)絡(luò)的社團結(jié)構(gòu)問題。因此,本文將已成熟的聚類算法應(yīng)用到復(fù)雜網(wǎng)絡(luò)社團識別問題上。本文的主要工作如下:(1)基于增強模塊度社團識別算法:首先,該算法應(yīng)用隨機游走理論把無向無權(quán)網(wǎng)絡(luò)通過預(yù)處理轉(zhuǎn)化為無向有權(quán)網(wǎng)絡(luò),預(yù)處理后的網(wǎng)絡(luò)社團之間的連邊權(quán)值小,社團內(nèi)部中連邊的權(quán)值大。然后,使用CNM算法對實際網(wǎng)絡(luò)進行劃分,并使用無向有權(quán)網(wǎng)絡(luò)的模塊度公式來衡量劃分結(jié)果的好壞。本文提出了一種將隨機游走理論與CNM算法結(jié)合的社團識別算法,其劃分結(jié)果表明這種算法可以有效地避免模塊度優(yōu)化時所產(chǎn)生的分辨率問題。將該算法應(yīng)用到人工網(wǎng)絡(luò)或社團結(jié)構(gòu)較為顯著的現(xiàn)實網(wǎng)絡(luò)中,識別出的社團效果較好。(2)基于聚類算法思想的社團結(jié)構(gòu)識別算法:基于邊的信息中心度,本文提出了節(jié)點親密度的概念,并構(gòu)建了節(jié)點親密度矩陣。然后,采用聚類思想對節(jié)點親密度矩陣進行聚類,從而形成了一種基于聚類思想的社團結(jié)構(gòu)發(fā)現(xiàn)新算法。鑒于聚類算法對初始值選取敏感,本文制訂了一些選取規(guī)則,有效地避免了此類問題。最后,通過經(jīng)典網(wǎng)絡(luò)模型證明了該算法的有效性。
[Abstract]:In nature, complex network systems can be found everywhere. Whether it is the economic system, the citation network system, the food chain network system or the biochemistry system that people can not perceive, these complex network systems all have their own properties and connections. In order to fully study these complex network systems, scholars abstract a model-complex network. In recent years, the rise of complex networks has attracted the attention of experts in related fields, and has quickly become the focus of their research. Through further research and analysis, scholars find that different real network models have the same characteristics. Community structure is a key feature in describing complex networks, and it is also the most common and key topological attribute in networks. The study of community structure not only has important theoretical significance, but also has practical application value. Community structure can help people better understand the topology of network, the function module of complex network, the hidden relationship between nodes, and predict the change trend of network system. In the process of community structure recognition in complex networks, modularity metric and its derived metrics play an important role, and give birth to a large number of important community recognition algorithms. However, the community structure of complex networks obtained by the general modular optimization method has the problem of resolution, which affects the accuracy and application breadth of the modular degree optimization method. Aiming at the resolution problem caused by modularity optimization, this paper proposes an enhanced modularity optimization method, which can effectively avoid the resolution problem. Because the division of community structure is similar to the idea of clustering algorithm, the method and theory of data mining can be used to study the problem of community structure in complex networks. Therefore, this paper applies the mature clustering algorithm to the complex network community recognition problem. The main work of this paper is as follows: (1) based on the enhanced modular degree community recognition algorithm: firstly, the algorithm applies random walk theory to transform the undirected unauthorized network into an undirected weighted network by preprocessing. After pretreatment, the weight of the connected edges is small and the weight of the connected edges in the communities is large. Then, the actual network is divided by CNM algorithm, and the module degree formula of undirected weighted network is used to measure the result of partition. In this paper, a community recognition algorithm based on random walk theory and CNM algorithm is proposed. The partition results show that this algorithm can effectively avoid the resolution problem caused by modularity optimization. The algorithm is applied to artificial network or real network with obvious community structure. (2) Community structure recognition algorithm based on clustering algorithm: edge based information center degree. In this paper, the concept of node affinity is proposed and the node affinity matrix is constructed. Then, the cluster idea is used to cluster the node affinity matrix, and a new community structure discovery algorithm based on clustering theory is formed. Since the clustering algorithm is sensitive to the selection of initial values, this paper formulates some selection rules to effectively avoid this kind of problem. Finally, the effectiveness of the algorithm is proved by classical network model.
【學(xué)位授予單位】：蘭州理工大學(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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