Time series of Internet AS-level topology graphs: four patterns and one   model
  Researchers have proposed a variety of Internet topology models. However almost all of them focus on generating one graph based on one single static source graph. On the other hand, Internet topology is evolving over time continuously with the addition and deletion of nodes and edges. If a model is based on all the topologies in the past, instead of one of them, it will be more accurate and closer to the real world topology. In this paper, we study the Internet As-level topology time-series from two different sources and find that both of them obey four same dynamic graph patterns. Then we propose a mode that can infer the topology in the future based on all the topologies in the past. Through theoretical and experimental analysis, we prove the topology that our model generates can match both the static and dynamic graph patterns. In addition, the parameters in the model are meaningful. Finally, we theoretically and experimentally prove that these parameters are directly related to some important graph characteristics. 
Lian-dong Liu and Ke Xu