复杂网络论文：复杂网络链路预测节点相似度指数弱连接

复杂网络论文：复杂网络链路预测节点相似度指数弱连接【中文摘要】自然界和人类社会中广泛存在着各种各样的复杂系统,而复杂系统可通过复杂网络来描述。复杂网络的研究将极大地促进复杂系统的研究与发展,对理解复杂系统的结构与功能具有重要的意义。近年来,复杂网络的研究正渗透到从物理学到生物学的众多不同学科,对复杂网络的定性特征与定量规律的深入探索、科学理解以及可能的应用,已经成为复杂系统或复杂性科学研究中一项极其重要的挑战性课题。链路预测是复杂网络中的一个新兴的研究方向,是指利用已知的网络节点和网络结构等信息预测网络中存在但尚未发现的未知链接和不存在但可能形成的未来链接。近年来,链路预测因其重要的理论价值和潜在的应用前景而广受关注,成为了复杂网络研究领域的研究热点之一。目前,链路预测的研究主要集中在无向无权网络,关于有向或加权网络的链路预测问题的研究较少。本论文以无向无权网络的链路预测算法为基础,分别发展了有向网络的链路预测算法和加权网络的链路预测改进算法。本论文共分四章,第一章简单介绍了复杂网络中链路预测及其研究意义。第二章回顾了无向无权网络中链路预测的研究进展。在第三章中,我们首先将12种针对无向网络的链路预测算法拓展有向网络的情况,建立起了基于局域连接信息的有向链路预测算法的基本框架。然后,基于有向网络模体的统计分析,我们构造了一种广义的共有邻居指数,同时也提出了一种两指数共同预测的结合指数。在10个真实有向网络中,我们对基于这些指数所建立的16种链路预测算法进行了测试和分析,得到了一些对实际应用

有一定指导意义的结论。特别地,归因于高的预测精度和低的计算复杂度,广义共有邻居指数和结合指数将有望在实际的链路信息挖掘中得到应用。在第四章,我们提出了一种适于加权网络链路预测的改进算法,在几个真实的加权网络中进行了测试,分析了强、弱链接对预测精度的影响,发现弱链接在实现链路的高精度预测方面具有比强链接更重要的作用。最后,我们对论文进行了总结,并对将来可能的研究方向进行了展望。

【英文摘要】Complex networks provide a qualitative description for various complex systemswhich exist extensively in nature and human society. The research of complex networksvastly boost the study of complex systems and is of great significance for understandingrelations between their structure and function. Recently, the research of complexnetworks is extended to a number of disciplines from physics to biology and others. Thedeeper analysis of the qualititative and quantitative characteristics of complexnetworks,accumulation of scientific knowledge and the mining of their potentialapplications are becoming an important and challenging subject for the research ofcomplex systems and complex science.As a new research direction of complex networks, link prediction is to predict themissing links which exist yet not been found and the future links which

would appearbased on the known information of network structure. Due to its theoretical significanceand potential applications, link prediction is becoming one of the hot areas of complexnetworks. Nowadays, most works of link prediction are focused on the unweighted andundirected networks, but the link prediction of weighted or directed networks is paid alittle attention. Based on the link prediction algorithms of unweighted and undirectednetworks, our thesis develops the link prediction algorithms of directed networks andimproves the ones of weighted networks.Our thesis consists of four chapters. The first chapter introduces the link predictionof complex networks and its significance of research. Chapter 2 reviews the researchprogress of the link prediction of unweighted and undirected networks. In chapter 3, wefirst extend the 11 link prediction algorithms for unweighted and undirected networks todirected networks, and establish the basic framework of directed link predictionalgorithms based on local information of networks. Then, based on the statistical analysisof directed networks’motifs, we construct the generalized common neighbour index, andat the same time propose a combined link prediction index. We test and analyze the 16link prediction algorithms based on these indices on 10 real