本文選題：復(fù)雜網(wǎng)絡(luò)　切入點(diǎn)：識(shí)別重要節(jié)點(diǎn)　出處：《西南大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來(lái),復(fù)雜網(wǎng)絡(luò)系統(tǒng)已經(jīng)融入到人們生產(chǎn)生活的方方面面。作為一個(gè)新興且活躍的科學(xué)研究領(lǐng)域,復(fù)雜網(wǎng)絡(luò)早已引入到在現(xiàn)實(shí)世界網(wǎng)絡(luò)的實(shí)證研究。目前,在計(jì)算機(jī)科學(xué)、社會(huì)科學(xué)、生物科學(xué)、管理科學(xué)等眾多領(lǐng)域得到了越來(lái)越多的人的重視。一方面,伴隨著復(fù)雜網(wǎng)絡(luò)的不斷發(fā)展,人類的生產(chǎn)生活質(zhì)量有了大幅度的提高和升華,并且為之帶來(lái)了極大的便利。但是另一方面,復(fù)雜網(wǎng)絡(luò)系統(tǒng)的運(yùn)行也對(duì)人類的生產(chǎn)生活帶來(lái)了一定的負(fù)面沖擊,比如疾病的快速傳播、大面積的停電事故、以及交通運(yùn)輸?shù)陌c瘓等等。因此,我們需要對(duì)各種復(fù)雜網(wǎng)絡(luò)系統(tǒng)有著更為深刻的認(rèn)識(shí)和分析,以便對(duì)可能造成的負(fù)面影響進(jìn)行預(yù)測(cè)、避免、控制等等。在眾多復(fù)雜網(wǎng)絡(luò)研究方向中,節(jié)點(diǎn)重要度評(píng)估已經(jīng)成為其研究發(fā)展中一個(gè)較為深遠(yuǎn)的方向。雖然目前已經(jīng)許多的中心性方法被提出來(lái)度量節(jié)點(diǎn)的重要度,但不同的中心性在各個(gè)方面或多或少都存在著一定的不足和局限性。由于不同的中心性的機(jī)制不同,而且有著不同的不足,因此,當(dāng)對(duì)同一個(gè)網(wǎng)絡(luò)使用不同的中心性進(jìn)行節(jié)點(diǎn)重要度評(píng)估時(shí),往往會(huì)得到不同的結(jié)果。為此,我們有必要對(duì)現(xiàn)有的中心性進(jìn)行改進(jìn),從而能全面有效的對(duì)復(fù)雜網(wǎng)絡(luò)節(jié)點(diǎn)重要度進(jìn)行評(píng)估。本文主要提出了三種不同的中心性算法對(duì)節(jié)點(diǎn)進(jìn)行重要度評(píng)估。首先將有效距離引入節(jié)點(diǎn)最短路徑的應(yīng)用中,用其代替?zhèn)鹘y(tǒng)的測(cè)地線和地理距離來(lái)衡量網(wǎng)絡(luò)節(jié)點(diǎn)的距離,并利用改進(jìn)后接近中心性對(duì)節(jié)點(diǎn)進(jìn)行重要度評(píng)估。然后提出了一種基于TOPSIS算法的多屬性決策模型的中心性算法,該算法將多個(gè)中心性作為多屬性進(jìn)行融合來(lái)評(píng)估節(jié)點(diǎn)重要度。最后,我們基于失效模式及影響分析模型,將復(fù)雜網(wǎng)絡(luò)的節(jié)點(diǎn)信息進(jìn)行建模來(lái)刻畫發(fā)生頻度、嚴(yán)重程度、檢測(cè)難易程度,并通過(guò)風(fēng)險(xiǎn)順序數(shù)來(lái)對(duì)節(jié)點(diǎn)進(jìn)行重要度評(píng)估。為了體現(xiàn)出本文提出的算法的有效性和實(shí)用性,我們都將這些算法應(yīng)用到真實(shí)的網(wǎng)絡(luò)中進(jìn)行對(duì)比實(shí)驗(yàn)。本文的工作主要包括以下幾個(gè)方面：(1)提出基于有效距離的接近中心性算法在真實(shí)的網(wǎng)絡(luò)中,往往會(huì)有孤立節(jié)點(diǎn)和單向邊,這會(huì)導(dǎo)致部分節(jié)點(diǎn)對(duì)的距離是無(wú)窮大,在此情況下則利用傳統(tǒng)接近中心性來(lái)評(píng)估節(jié)點(diǎn)重要度是無(wú)效的。針對(duì)此問(wèn)題,我們引入有效距離,來(lái)代替?zhèn)鹘y(tǒng)的測(cè)地線和地理距離來(lái)度量網(wǎng)絡(luò)節(jié)點(diǎn)的距離。該模型不但解決了傳統(tǒng)接近中心性失效的問(wèn)題,還能廣泛應(yīng)用于加權(quán)網(wǎng)絡(luò)中,而且更加合理的表示了網(wǎng)絡(luò)節(jié)點(diǎn)信息流的傳輸過(guò)程。(2)提出基于TOPSIS模型的中心性算法TOPSIS算法是一種被廣泛應(yīng)用的多屬性決策算法,它能有效地融合多個(gè)有差異的屬性,并得出一組接近理想最優(yōu)解的排序。由于各種中心性算法都存在著種種缺點(diǎn),并且不同中心性會(huì)產(chǎn)生不同的評(píng)估結(jié)果,因此我們認(rèn)為有必要提出一種折衷的算法來(lái)融合這些差異以及克服單一中心性所存在的缺點(diǎn)。我們將度中心性、接近中心性和介數(shù)中心性這三個(gè)最為基礎(chǔ)的中心性作為多個(gè)屬性引入到TOPSIS多屬性決策模型中,將融合后的中心性作為網(wǎng)絡(luò)節(jié)點(diǎn)的重要度評(píng)估算法。該算法不僅解決了這三個(gè)中心性各自存在的缺陷,還有效地將它們的差異進(jìn)行折衷融合。并且首次將工程評(píng)估中的TOPSIS算法引入到復(fù)雜網(wǎng)絡(luò)系統(tǒng)中,對(duì)跨學(xué)科領(lǐng)域研究有著積極的影響。(3)提出基于失效模式及影響分析模型的中心性算法失效模式及影響分析是一種可靠性設(shè)計(jì)的重要方法,它通過(guò)由發(fā)生頻度、嚴(yán)重程度、檢測(cè)難易程度得出的風(fēng)險(xiǎn)順序數(shù)來(lái)對(duì)模式進(jìn)行評(píng)估。我們利用網(wǎng)絡(luò)的結(jié)構(gòu)和節(jié)點(diǎn)的信息進(jìn)行建模來(lái)刻畫發(fā)生頻度、嚴(yán)重程度、檢測(cè)難易程度。我們認(rèn)為如果一個(gè)節(jié)點(diǎn)的入度越大,則表明其他節(jié)點(diǎn)發(fā)生故障時(shí)影響到該節(jié)點(diǎn)的機(jī)會(huì)就越大,那么這個(gè)節(jié)點(diǎn)發(fā)生“失效”的概率就越高。同時(shí),倘若一個(gè)節(jié)點(diǎn)到其他所有節(jié)點(diǎn)的有效距離越短,則表明該節(jié)點(diǎn)失效后影響的傳播就越廣,那么這個(gè)節(jié)點(diǎn)失效的嚴(yán)重程度就越大。在此模型中,我們定義了網(wǎng)絡(luò)節(jié)點(diǎn)的熵的概念。因?yàn)樾畔㈧乇硎镜氖窍到y(tǒng)或者個(gè)體的不確定性,因此我們認(rèn)為如果一個(gè)節(jié)點(diǎn)的熵值越大,則這個(gè)節(jié)點(diǎn)在網(wǎng)絡(luò)中所處的結(jié)構(gòu)也就越復(fù)雜,那么對(duì)這個(gè)節(jié)點(diǎn)進(jìn)行失效探測(cè)的難易程度也就越難。最后,我們根據(jù)新的模型得出的風(fēng)險(xiǎn)順序數(shù)對(duì)節(jié)點(diǎn)進(jìn)行重要度評(píng)估。風(fēng)險(xiǎn)順序數(shù)值越大,則節(jié)點(diǎn)越重要。
[Abstract]:In recent years, the complex network system has been integrated into people's lives. As a new and active field of scientific research, has been introduced into the empirical research of complex networks in the real world network. At present, in computer science, social science, biological science, management science and other fields has been more and more people attention. On the one hand, with the development of complex network, the production of human life quality has been greatly improved and sublimation, and brings great convenience to them. But on the other hand, the complex network system for the production of human life has brought certain negative impact, such as the rapid spread of the disease the large area blackout, and paralyzed transportation etc.. Therefore, we need to have a more profound understanding and analysis of the complex network system, so as to possible The negative effects of prediction, avoid, control and so on. In many directions in the study of complex networks, node importance evaluation has become a more profound direction of its research and development. Although the central approach has been proposed to measure many important node, but not the same center in all aspects are more or less shortcomings and limitations. Because of the different mechanism, but also have different problems, therefore, when the center of different use on the same network node importance evaluation, tend to get different results. Therefore, it is necessary for us to improve the existing center thus, comprehensive and effective on the node importance evaluation. This paper presents three different centrality algorithm on node importance evaluation. The effective distance of nodes is introduced The application of the shortest path, to replace the traditional wire and geographic distance measurement to measure the distance of network nodes, and using the improved close centrality of node importance evaluation. Then put forward a central algorithm of multi attribute decision making model based on TOPSIS algorithm, this algorithm will be more as the center multi attribute fusion to evaluate the node importance. Finally, we model the failure mode and effect analysis based on the node information of complex network model to describe the frequency, severity, detection of the degree of difficulty, and the number of order through risk assessment on the node. In order to demonstrate the validity and practicality of the proposed in the algorithm, we will apply these algorithms to real network experiments. The main work of this paper includes the following aspects: (1) proposed to effectively based on distance The center of algorithm in real network, often isolated nodes and one side, this will cause the distance on the part of the node is infinite, in this case is close to the center of the traditional evaluation of node importance is invalid. To solve this problem, we introduce the effective distance, to replace the ground and geographic distance measurement the traditional network node to measure the distance. This model not only solves the problem of the traditional center close to failure, but also widely used in the weighted network, and more reasonable representation of the transmission process of the network node information flow. (2) the center of TOPSIS algorithm based on TOPSIS model is a widely used the algorithm of multi attribute decision making, it can effectively combine multiple different attributes, and draw a set close to the ideal optimal solution sorting algorithm. Due to the variety of center there are many shortcomings, and in different The mind will produce different results, so we think it is necessary to put forward a compromise algorithm to fuse these differences and overcome the shortcomings of a single center. We will degree centrality, closeness centrality and betweenness centrality of the three most basic center for multiple attribute into TOPSIS multi attribute decision making model, the center of fusion as an important evaluation algorithm of network nodes. The algorithm not only solves the defects of the three centers of their existence, but also effectively will compromise their differences and fusion. For the first time in the TOPSIS project evaluation algorithm is introduced to the complex network system, a a positive impact on the interdisciplinary field. (3) put forward the algorithm analysis model of failure mode and effect of failure mode and effect analysis is an important method of reliability design based on it through The frequency of occurrence, severity, detection of the degree of difficulty that the risk assessment of the number of sequential patterns. We use the structure and node of the network information modeling to describe the occurrence, severity, degree of difficulty detection. We think that if a node degree is bigger, that other node failures influence to the node of the greater the chance, then the node failure probability is higher. At the same time, if a node to all other nodes of the effective distance is shorter, indicates that the propagation effect after node failure is bigger, the severity of the node failure in this model is greater., we define the concept of network node entropy. Because information entropy represents the system or individual uncertainty, so we think that if a node of the greater entropy of the nodes in the network The more complex the structure is, the harder it is to detect the failure of the node. Finally, we evaluate the importance of the node according to the number of risk sequence obtained by the new model. The greater the risk order value is, the more important the node is.

【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O157.5

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本文編號(hào)：1608527