Rank-based deactivation model for networks with age

We study the impact of age on network evolution which couples addition of new nodes and deactivation of old ones. During evolution, each node experiences two stages: active and inactive. The transition from the active state to the inactive one is based on the rank of the node. In this paper, we adopt age as a criterion of ranking, and propose two deactivation models that generalize previous researches. In model A, the older active node possesses the higher rank, whereas in model B, the younger active node takes the higher rank. We make comparative study between the two models through the node-degree distribution.