【作者】 李金霞； 耿显民；

【Author】 Jinxia Li, Xianmin Geng (College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China)

【机构】 南京航空航天大学理学院；

【摘要】 根据引文网发展形成的实际过程,以解析方法研究引文关系的随机演化网络,在考虑寿命和随机演化的情况下,得到引文网是无标度网络。在引文网络中,结点为发表的文章,连线为发表的文章引用之前已经发表的文章这一关系。由于一篇文章在发表时,它要引用网络中已经存在的结点,同时网络中有一部分结点被它所引用,因此,具有引用与被引用两种关系的引文网是有向网络。[8]中研究了ISI中的783339篇文章的引用关系和PRD在1975与1994年期间发表的24296篇文章的引用关系的分布。通过数据模拟,结果显示已经发表的文章被引用k次的概率p(k)服从幂律分布p(k)-k-γ,其中标度指数γ≈3;所有结点具有很大边数的概率以幂律的速度减小。不难看到由于大多数发表的文章随着时间的推移而渐渐被忘记或是重要性减小,所以一篇文章被引用的概率会随着存在于网络的时间的增大而减小。又由于一篇新发表的文章,通过被引用的次数的增多而越来越受关注,从而被认可。因此,引文网模型是结点的被引用概率随其寿命的变化而变化的网络。进一步,在一给定时刻,网络中一结点(文章)被连接(被引用)的概率与该结点的入度(文章被引用次数)有关。针对这种现象,很多文章考虑了结点寿命问题, 给出了不同的带有寿命的偏好概率[9,10,11],通过数据模拟指出,在满足一定条件的前提下,引文网满足[8]中的结论。本文在演化过程的偏好依附随机网络模型[1]的基础上,引入一个表示新结点所带边数为ξ的随机变量,考虑网络结点寿命以(t-ti)-△衰减,其中t-ti为结点i在网络中存在的时间;建立了带有寿命衰减的偏好依附随机网络模型,然后进行了严密的数学推导,得出了p(k)服从幂律分布 k-γ,即Scale-free的结论,其中的标度指数γ≈3。更多还原

【Abstract】 In this paper, according to the actual process how a citation network forms, we study random evolution model of citation networks. In the case of the network random evolution with aging, we obtain that citation networks are scale-free. In citation networks, the nodes are published papers and a link is formed if one paper cites another paper published previously. Actually, citation is possible only to papers that have been published previously, so that the network is directed. In Ref. [8] the citation distribution of 783,339 papers cataloged by Institute of Scientific Information and also the 24,296 papers published in Physical Review D between 1975 and 1994 was studied. It was found that the probability p(k) that a particular paper is cited k times follows a power-law distribution p(k)~ k-γ with exponent γ ≈3 .And it was also found that the incoming degree distribution of the citation network is scale-free. Also, since most of the papers are gradually forgotten or become irrelevant, the probability that a particular paper is cited should decrease in time unless it is of utmost importance. And, a young paper, which is undergoing recognition, gains increasing attention through citations. Hence, the model of a citation network should be one in which aging of the papers occur such that the probability of a paper getting cited depends on its age. The aging of the nodes in a citation network has been considered in Ref. [9,10,11]. In this paper, in the base of the study on the random networks model [1] with preferential attachment, we establish the random model of network with preferential attachment and aging decay. We consider that the number of edges which the new node link is a random variable ξ(ω), we also consider the aging of network nodes decays as (t - ti)-△; where t - ti denotes the time when node i exist in the networks. Then we use the analytic method to deduce that the networks model is scale-free.更多还原