Modeling the time-periodicity of in-degree distributions in scientific citation networks

In a range of citation networks, the in-degree distributions boast time-periodicity---the distributions of citations per article published each year present similar scale-free tails. This phenomenon can be regarded as a consequence of the emergence of 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 time-periodicity of the in-degree distributions of the empirical data, and accounts for the presence of citation burst as well. Moreover, a reasonable explanation for the emergence of the scale-free tails by regarding the citation behavior between articles as a "yes/no" experiment is presented. The model can also predict the time-periodicity of the local clustering coefficients, which indicates that the model is a good tool in researches on the evolutionary mechanism of citation networks.