A geometric graph model of citation networks with linearly growing   node-increment
  Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic influence scopes of the papers are denoted through specific geometric areas related to time and space. In the model, nodes (papers) are uniformly and randomly sprinkled onto a cluster of circles of the Minkowski space whose centers are on the time axis. Edges (citations) are linked according to an influence mechanism which indicates that an existing paper will be cited by a new paper located in its influence zone. Considering the citations among papers in different disciplines, an interdisciplinary citation mechanism is added to the model in which some papers with a small probability of being chosen will cite some existing papers randomly and uniformly. Different from most existing models that only study the power-law tail of the in-degree distribution, this model also characterizes the overall in-degree distribution. Moreover, it presents the description of some other important statistical characteristics of real networks, such as in- and out-assortativity, giant component and clear community structure. Therefore, it is reasonable to believe that a good example is provided in the paper to study real networks by geometric graphs. 
Qi Liu, Zheng Xie, Engming Dong, Jianping Li
physics.soc-ph cs.DL