Modeling And Analyzing Scientific Citation Networks Via Geometric Graphs

A scientific citation network is defined using a set of articles as nodes with directed edges representing the citations from one article to another article.The research of them can help scientists analyze the emergence and propagation of academic thoughts,track hot topics of scientific research,master the knowledge vein and understand the latest research results.In citation networks,engendering citations between papers is effected by their novelty,importance and readability,of which the content relativity of papers is a precondition.Since the relativity of their content can be abstracted into a kind of geometric distance,the geometric graph is applied into the research of citation networks in this paper.Moreover,citation between papers can be regarded as a causal relationship,so geometric graphs are built on a cluster of circles located in a(2+1)-dimensional Minkowski space.The main work is as follows:(1)A geometric model is built to study the evolutionary mechanism of citation networks.In the model,nodes(papers)with geometric areas(academic influence)are located on these circles randomly and uniformly.Edges(citation)between articles are linked according to an influence mechanism which indicates that an existing article will be cited by a new article located in its influence zone.Considering the citations among articles in different disciplines,an interdisciplinary citation mechanism is added to the model in which some articles with a small probability of being chosen will cite some existing articles randomly and uniformly.The model presents the description of some important statistical characteristics of real networks like the overall in-degree distribution.The good results show that these two mechanisms are reasonable.(2)We analyse the statistical features of some data,e.g.PNAS,Nature,mined from Web of Science and find that these features are self-similar in the time dimension.The self-similarity of the in-degree distribution are treated as a consequence of the emergence of the hot topics and the existence of the “burst” phenomenon.With this inference considered,a geometric model based on our previous study is established,in which the sizes of the influence zones of nodes follow the same power-law distribution and decrease with their ages.The model successfully reproduces the self-similarity of the in-degree distributions of the empirical data,and accounts for the presence of citation burst as well.Moreover,the clustering coefficient as a function of in-degree k is also self-similar in the time dimension,which indicates that the mechanism in the model is sound.