本文選題：加權(quán)網(wǎng)絡(luò) + 多重分形分析��； 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：本文的研究對象為加權(quán)網(wǎng)絡(luò)和時序網(wǎng)絡(luò),這兩類網(wǎng)絡(luò)是無權(quán)網(wǎng)絡(luò)的推廣。在討論加權(quán)網(wǎng)絡(luò)時,本文關(guān)注的是分形和多重分形性質(zhì)的分析,在討論時序網(wǎng)絡(luò)時,本文則討論的是這類網(wǎng)絡(luò)上節(jié)點重要性的評估方法。近些年來,加權(quán)網(wǎng)絡(luò)因為它能更好刻畫現(xiàn)實復(fù)雜系統(tǒng)的結(jié)構(gòu)特性而受到很多研究者的關(guān)注,有關(guān)加權(quán)網(wǎng)絡(luò)的結(jié)構(gòu)研究中,涉及到加權(quán)網(wǎng)絡(luò)多重分形性質(zhì)方面的研究工作比較少。在本文中,受到Koch網(wǎng)絡(luò)和Koch島分形的啟發(fā),一種新型加權(quán)Koch網(wǎng)絡(luò)模型被提出來作為研究加權(quán)網(wǎng)絡(luò)的模型框架,隨后本文從拓?fù)涮匦院吞卣髦底V方面研究了這種新型加權(quán)Koch網(wǎng)絡(luò),接著本文重點研究了新型加權(quán)Koch網(wǎng)絡(luò)的分形和多重分形特性,本文發(fā)現(xiàn)新提出的網(wǎng)絡(luò)是分形網(wǎng)絡(luò)并且具有多重分形測度,隨后這些研究方法被應(yīng)用來研究幾個實際復(fù)雜網(wǎng)絡(luò),研究結(jié)果表明實際的加權(quán)復(fù)雜網(wǎng)絡(luò)也具有無權(quán)復(fù)雜網(wǎng)絡(luò)的一些類似拓?fù)湫再|(zhì),但是這兩類網(wǎng)絡(luò)的這些性質(zhì)之間沒有必然聯(lián)系。受到數(shù)據(jù)的驅(qū)動以及各種應(yīng)用的需求,時序網(wǎng)絡(luò)中節(jié)點重要性的評估這一問題受到越來越多的學(xué)者關(guān)注。傳統(tǒng)的方法主要針對的是靜態(tài)網(wǎng)絡(luò),而且在分析這類問題時過多考慮了網(wǎng)絡(luò)的拓?fù)涮匦?而對節(jié)點的動力學(xué)特性關(guān)注太少。本文主要關(guān)注網(wǎng)絡(luò)節(jié)點的動力學(xué)特性,并把靜態(tài)網(wǎng)絡(luò)中的動態(tài)敏感中心性指標(biāo)推廣到時序網(wǎng)絡(luò),在三個實際網(wǎng)絡(luò)數(shù)據(jù)數(shù)據(jù)集和一個理論網(wǎng)絡(luò)數(shù)據(jù)集上建立SIR模型仿真,實驗表明本文推廣的方法比一些靜態(tài)網(wǎng)絡(luò)中常用的指標(biāo)如度中心性、接近中心性、介數(shù)中心性以及它們的在時序網(wǎng)絡(luò)中的推廣指標(biāo)都要準(zhǔn)確。最后,作為一個應(yīng)用,所推廣的動態(tài)敏感中心性指標(biāo)被用來研究節(jié)點的時序因素對時序網(wǎng)絡(luò)傳播行為的影響,結(jié)果表明網(wǎng)絡(luò)節(jié)點的拓?fù)涮匦院蜁r序都會對傳播造成影響,而且當(dāng)網(wǎng)絡(luò)傳播率β接近網(wǎng)絡(luò)的傳播閾值βc時,時序因素產(chǎn)生的影響將變小。
[Abstract]:The research object of this paper is weighted network and time series network, which are the extension of weighted network. In discussing weighted networks, this paper focuses on the analysis of fractal and multifractal properties, and discusses the evaluation methods of node importance in time series networks. In recent years, many researchers have paid attention to weighted networks because they can better describe the structural characteristics of complex systems in reality. In the study of weighted networks, there are few researches on multifractal properties of weighted networks. In this paper, inspired by Koch network and Koch island fractal, a new weighted Koch network model is proposed as a model framework to study the weighted network, and then this new weighted Koch network is studied in terms of topological characteristics and eigenvalue spectrum. Then the fractal and multifractal properties of the new weighted Koch network are studied. It is found that the new network is a fractal network and has multifractal measures. Then these methods should be used to study several real complex networks. The results show that the actual weighted complex networks also have some similar topological properties of unweighted complex networks, but there is no necessary relation between these properties of these two kinds of networks. Driven by data and required by various applications, the importance of nodes in time series networks has attracted more and more attention. The traditional method is mainly aimed at static network, and the topology of the network is considered too much when analyzing this kind of problem, but little attention is paid to the dynamic characteristics of nodes. This paper mainly focuses on the dynamic characteristics of network nodes, and extends the dynamic sensitivity center index of static network to time series network, and establishes Sir model simulation on three actual network data sets and one theoretical network data set. The experiments show that the proposed method is more accurate than some commonly used indexes in static networks such as degree centrality, proximity centrality, intermediate centrality and their generalization indexes in time series networks. Finally, as an application, the extended dynamic sensitivity centrality index is used to study the influence of the timing factors of nodes on the propagation behavior of time series networks. The results show that the topological characteristics and timing of network nodes will have an impact on the propagation. Moreover, when the network propagation rate 尾 is close to the network propagation threshold 尾 c, the influence of time series factors will be reduced.
【學(xué)位授予單位】：湘潭大學(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：1997955