本文關(guān)鍵詞： 復(fù)雜網(wǎng)絡(luò) 多傳播源 廣義接近中心性 K-means　出處：《安徽大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來,對復(fù)雜網(wǎng)絡(luò)的研究已經(jīng)受到計(jì)算機(jī)、數(shù)學(xué)、經(jīng)濟(jì)學(xué)、傳播學(xué)和生物學(xué)等不同學(xué)科領(lǐng)域的關(guān)注,網(wǎng)絡(luò)的結(jié)構(gòu)與動(dòng)力學(xué)是復(fù)雜網(wǎng)絡(luò)科學(xué)的兩個(gè)最基本問題。對于網(wǎng)絡(luò)結(jié)構(gòu)的探測包括:網(wǎng)絡(luò)的社團(tuán)劃分,關(guān)鍵節(jié)點(diǎn)的識別,鏈路預(yù)測等,其中許多學(xué)者都致力于網(wǎng)絡(luò)中有影響力傳播源識別的研究,即找到網(wǎng)絡(luò)中的一個(gè)或者多個(gè)節(jié)點(diǎn)使得這些節(jié)點(diǎn)對網(wǎng)絡(luò)的影響最大。這一課題在實(shí)際生活中對抑制疫情擴(kuò)散,加速信息傳播和推廣新產(chǎn)品等都具有重要戰(zhàn)略意義。本文主要研究的是尋找一組節(jié)點(diǎn)使得這一組節(jié)點(diǎn)對網(wǎng)絡(luò)的影響最大。一個(gè)節(jié)點(diǎn)到網(wǎng)絡(luò)中所有節(jié)點(diǎn)距離和越小則這個(gè)節(jié)點(diǎn)越重要,由此我們想到當(dāng)一組節(jié)點(diǎn)到網(wǎng)絡(luò)中所有節(jié)點(diǎn)距離和最小時(shí)這組節(jié)點(diǎn)對整個(gè)網(wǎng)絡(luò)來說比較重要。基于此思想本文主要有以下兩方面工作:1.由節(jié)點(diǎn)的接近中心性推廣到一組節(jié)點(diǎn)到所有節(jié)點(diǎn)的距離越短越好,進(jìn)而提出廣義接近中心性。因此尋找一組最重要節(jié)點(diǎn)的問題轉(zhuǎn)化為尋找目標(biāo)函數(shù)的最優(yōu)解,之后我們證明可以用K-means聚類模型近似求目標(biāo)函數(shù)的最小值。2.用single-contact SIR模型和all-contact SIR及謠言傳播模型在實(shí)際網(wǎng)絡(luò)上進(jìn)行模擬實(shí)驗(yàn),并與度、介數(shù)、K-核、著色、最優(yōu)滲流等方法進(jìn)行比較分析。結(jié)果表明:廣義接近中心性指標(biāo)在signal-contact SIR模型、all-contact SIR模型和謠言傳播模型上都表現(xiàn)出較好的結(jié)果。
[Abstract]:In recent years, the research on complex networks has been concerned by computer, mathematics, economics, communication and biology. The structure and dynamics of network are two basic problems in complex network science. The detection of network structure includes community division of network, identification of key nodes, link prediction and so on. Many of them are devoted to the research of influential source identification in the network. That is to find one or more nodes in the network to make these nodes have the greatest impact on the network. This problem in real life to curb the spread of the epidemic. It is of great strategic significance to accelerate the dissemination of information and promote new products. In this paper, the main research is to find a set of nodes to make this group of nodes have the greatest impact on the network. A node to all nodes in the network and the smaller the distance. The more important this node is. From this, we think that when a group of nodes to all nodes in the network and minimum distance, this group of nodes for the entire network is more important. Based on this idea, this paper mainly has the following two aspects of work:. 1. The shorter the distance from a group of nodes to all nodes, the better. The problem of finding a group of most important nodes is transformed into finding the optimal solution of the objective function. Then we prove that the K-means clustering model can be used to approximate the minimum value of the objective function. 2.Using single-contact SIR model and all-contact model. SIR and rumor propagation model are simulated on the actual network. The results show that the generalized approach to centrality is based on the signal-contact SIR model, and is compared with the methods of degree, medium K- kernels, coloring and optimal percolation. Both all-contact SIR model and rumor propagation model show good results.
【學(xué)位授予單位】：安徽大學(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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