復(fù)雜網(wǎng)絡(luò)的某些性質(zhì)研究及其應(yīng)用
發(fā)布時(shí)間：2018-09-18 20:40
【摘要】：自從Watts,Strogatz 1998年發(fā)現(xiàn)真實(shí)網(wǎng)絡(luò)的小世界特性以來(lái),復(fù)雜網(wǎng)絡(luò)融合了圖論、工程數(shù)學(xué)、計(jì)算機(jī)理論、社會(huì)科學(xué)等學(xué)科的有關(guān)理論與成果,已成為了一門(mén)單獨(dú)的學(xué)科。經(jīng)過(guò)十多年的研究,科學(xué)家們已經(jīng)發(fā)現(xiàn)了一些典型復(fù)雜網(wǎng)絡(luò)模型如小世界網(wǎng)絡(luò)模型、無(wú)標(biāo)度網(wǎng)絡(luò)模型、確定性小世界網(wǎng)絡(luò)模型等,同時(shí)也發(fā)現(xiàn)了這些典型網(wǎng)絡(luò)模型的一些主要特性。本文圍繞復(fù)雜網(wǎng)絡(luò)的小世界現(xiàn)象,針對(duì)典型復(fù)雜網(wǎng)絡(luò)模型重點(diǎn)研究了網(wǎng)絡(luò)節(jié)點(diǎn)度序列長(zhǎng)度特性、電阻距離特性及其應(yīng)用;基于代數(shù)圖論中的凱萊圖(Cayley)模型在隨機(jī)化加邊后也同樣具有復(fù)雜網(wǎng)絡(luò)的小世界特性,論文結(jié)合無(wú)線傳感器網(wǎng)絡(luò)和數(shù)據(jù)中心網(wǎng)絡(luò)的應(yīng)用需求,同時(shí)研究了基于代數(shù)圖論的具有小世界特性的復(fù)雜網(wǎng)絡(luò)模型及應(yīng)用。論文主要成果如下:(1)在肖文俊等人提出復(fù)雜網(wǎng)絡(luò)度序列長(zhǎng)度新特性的基礎(chǔ)上,論文從理論上證明了具有擴(kuò)展冪律分布、泊松分布、指數(shù)分布的復(fù)雜網(wǎng)絡(luò)模型的度序列長(zhǎng)度的新特性:即度序列長(zhǎng)度l與log_2N是同級(jí)別的結(jié)論,進(jìn)一步完善了肖文俊等人的結(jié)論。實(shí)驗(yàn)仿真結(jié)果及現(xiàn)實(shí)網(wǎng)絡(luò)的數(shù)據(jù)驗(yàn)證了該結(jié)論的有效性。該結(jié)論從理論上解釋了為什么現(xiàn)實(shí)世界的網(wǎng)絡(luò)直徑不大的問(wèn)題,可以作為復(fù)雜網(wǎng)絡(luò)的基本特性之一,同時(shí)論文提出了基于復(fù)雜網(wǎng)絡(luò)的度序列長(zhǎng)度的復(fù)雜網(wǎng)絡(luò)模型。針對(duì)復(fù)雜網(wǎng)絡(luò)的搜索問(wèn)題,論文完成了最短路徑算法和最大度算法的仿真實(shí)驗(yàn),結(jié)果表明在復(fù)雜網(wǎng)絡(luò)中基于最大度的搜索算法相比基于最短路徑的搜索算法更有效。(2)論文研究了復(fù)雜網(wǎng)絡(luò)中的電阻距離特性及其在社團(tuán)劃分中應(yīng)用的需求,提出了結(jié)合節(jié)點(diǎn)中心性指標(biāo)與電阻距離的社團(tuán)劃分算法。論文選擇了節(jié)點(diǎn)度中心性、接近度指標(biāo)、特征向量、聚類(lèi)系數(shù)及最短路徑等5類(lèi)節(jié)點(diǎn)中心性指標(biāo),基于模擬網(wǎng)絡(luò)、空手道網(wǎng)絡(luò)和寬吻海豚網(wǎng)絡(luò)等三種網(wǎng)絡(luò)進(jìn)行了仿真實(shí)驗(yàn),隨后論文將電阻距離引入到Kernighan-Lin(KL)算法和Fast Newman(FN)算法中,實(shí)驗(yàn)結(jié)果表明結(jié)合節(jié)點(diǎn)度中心性與電阻距離的社團(tuán)劃分算法及基于電阻距離的KL算法能準(zhǔn)確劃分三個(gè)實(shí)驗(yàn)網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu),但其它基于電阻距離的社團(tuán)劃分算法只能正確劃分部分實(shí)驗(yàn)網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu),存在一定的誤差。(3)基于復(fù)雜網(wǎng)絡(luò)模型的小世界特性的啟發(fā),論文結(jié)合基于代數(shù)圖論中的Cayley理論與復(fù)雜網(wǎng)絡(luò)理論,針對(duì)無(wú)線傳感器網(wǎng)絡(luò)節(jié)點(diǎn)動(dòng)態(tài)變化及虛擬路由的實(shí)際需求,提出了具有小世界特性的CayleyDHT模型,并在該模型的基礎(chǔ)上提出了CayleyDHTVCP路由協(xié)議,仿真實(shí)驗(yàn)表明該協(xié)議具有較好路由的效率和魯棒性。(4)針對(duì)目前數(shù)據(jù)中心網(wǎng)絡(luò)需要利用廉價(jià)設(shè)備構(gòu)建的趨勢(shì),論文分析了現(xiàn)有數(shù)據(jù)中心網(wǎng)絡(luò)結(jié)構(gòu)的優(yōu)缺點(diǎn),應(yīng)用基于代數(shù)圖論中的Cayley圖與復(fù)雜網(wǎng)絡(luò)理論,提出了基于數(shù)據(jù)中心網(wǎng)絡(luò)的C~3Cube模型,并在此模型的基礎(chǔ)上,提出了基于C~3Cube路由協(xié)議及容錯(cuò)協(xié)議,仿真實(shí)驗(yàn)表明該協(xié)議的有效性,可以有效地解決利用廉價(jià)設(shè)備構(gòu)建數(shù)據(jù)中心網(wǎng)絡(luò)的問(wèn)題。
[Abstract]:Since Watts and Strogatz discovered the small-world properties of real networks in 1998, complex networks have become a separate discipline, fusing the theories and achievements of graph theory, engineering mathematics, computer theory, social science and other disciplines. Bounded network model, scale-free network model, deterministic small-world network model and so on, and some main characteristics of these typical network models are also found. The Cayley model in number graph theory also has the small-world characteristics of complex networks after randomized edge addition. This paper combines the application requirements of wireless sensor networks and data center networks, and studies the complex network model with small-world characteristics based on algebraic graph theory and its application. On the basis of the new characteristics of degree sequence length proposed by Wen Jun et al, this paper theoretically proves the new characteristics of degree sequence length of complex network model with extended power law distribution, Poisson distribution and exponential distribution: that the length of degree sequence L is the same level as log_2N, which further perfects the conclusion of Xiao Wenjun et al. The validity of this conclusion is validated by real results and real network data. This conclusion explains why the diameter of real world network is not large and can be used as one of the basic characteristics of complex network. At the same time, a complex network model based on the length of degree sequence of complex network is proposed. The simulation results show that the algorithm based on maximum path is more effective than the algorithm based on shortest path in complex networks. (2) The resistance distance characteristics in complex networks and its application requirements in community partitioning are studied, and the joint nodes are proposed. Five kinds of node centrality indexes, such as node centrality, proximity index, eigenvector, clustering coefficient and shortest path, are selected in this paper. Three kinds of network are simulated based on Simulation network, karate network and bottlenose dolphin network. In Kernighan-Lin (KL) algorithm and Fast Newman (FN) algorithm, experimental results show that the community partitioning algorithm based on nodal centrality and resistance distance and KL algorithm based on resistance distance can accurately partition the community structure of three experimental networks, but other community partitioning algorithms based on resistance distance can only partition part of the experimental network correctly. (3) Inspired by the small-world characteristics of complex network model, this paper proposes a Cayley DHT model with small-world characteristics, which combines the Cayley theory based on algebraic graph theory with the complex network theory, aiming at the dynamic changes of wireless sensor network nodes and the actual needs of virtual routing. A Cayley DHTVCP routing protocol is proposed on the basis of the proposed model, and the simulation results show that the protocol has good routing efficiency and robustness. (4) Aiming at the trend that the current data center network needs to use cheap equipment to build, this paper analyzes the advantages and disadvantages of the existing data center network structure, and applies the Cayley diagram based on algebraic graph theory and complex network. Based on the network theory, a C~3Cube model based on data center network is proposed. Based on this model, a C~3Cube routing protocol and fault-tolerant protocol are proposed. Simulation results show that the protocol is effective and can effectively solve the problem of constructing data center network with cheap equipment.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O157.5
[Abstract]:Since Watts and Strogatz discovered the small-world properties of real networks in 1998, complex networks have become a separate discipline, fusing the theories and achievements of graph theory, engineering mathematics, computer theory, social science and other disciplines. Bounded network model, scale-free network model, deterministic small-world network model and so on, and some main characteristics of these typical network models are also found. The Cayley model in number graph theory also has the small-world characteristics of complex networks after randomized edge addition. This paper combines the application requirements of wireless sensor networks and data center networks, and studies the complex network model with small-world characteristics based on algebraic graph theory and its application. On the basis of the new characteristics of degree sequence length proposed by Wen Jun et al, this paper theoretically proves the new characteristics of degree sequence length of complex network model with extended power law distribution, Poisson distribution and exponential distribution: that the length of degree sequence L is the same level as log_2N, which further perfects the conclusion of Xiao Wenjun et al. The validity of this conclusion is validated by real results and real network data. This conclusion explains why the diameter of real world network is not large and can be used as one of the basic characteristics of complex network. At the same time, a complex network model based on the length of degree sequence of complex network is proposed. The simulation results show that the algorithm based on maximum path is more effective than the algorithm based on shortest path in complex networks. (2) The resistance distance characteristics in complex networks and its application requirements in community partitioning are studied, and the joint nodes are proposed. Five kinds of node centrality indexes, such as node centrality, proximity index, eigenvector, clustering coefficient and shortest path, are selected in this paper. Three kinds of network are simulated based on Simulation network, karate network and bottlenose dolphin network. In Kernighan-Lin (KL) algorithm and Fast Newman (FN) algorithm, experimental results show that the community partitioning algorithm based on nodal centrality and resistance distance and KL algorithm based on resistance distance can accurately partition the community structure of three experimental networks, but other community partitioning algorithms based on resistance distance can only partition part of the experimental network correctly. (3) Inspired by the small-world characteristics of complex network model, this paper proposes a Cayley DHT model with small-world characteristics, which combines the Cayley theory based on algebraic graph theory with the complex network theory, aiming at the dynamic changes of wireless sensor network nodes and the actual needs of virtual routing. A Cayley DHTVCP routing protocol is proposed on the basis of the proposed model, and the simulation results show that the protocol has good routing efficiency and robustness. (4) Aiming at the trend that the current data center network needs to use cheap equipment to build, this paper analyzes the advantages and disadvantages of the existing data center network structure, and applies the Cayley diagram based on algebraic graph theory and complex network. Based on the network theory, a C~3Cube model based on data center network is proposed. Based on this model, a C~3Cube routing protocol and fault-tolerant protocol are proposed. Simulation results show that the protocol is effective and can effectively solve the problem of constructing data center network with cheap equipment.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O157.5
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