A Geometric Graph Model of Citation Networks with Linearly Growing Node-Increment

Due to the fact that the numbers of annually published papers in some citation networks have witnessed a linear growth, a geometric model is thus raised to reproduce 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 scale-free tail of the in-degree distribution, this model characterizes the overall in-degree distribution. Moreover, the model can also predict the scale-free tail of the out-degree distribution, which indicates that the model is a good tool in researches on the evolutionary mechanism of citation networks.