All the existing real world networks are evolving, hence, study of traffic dynamics in these enlarged networks is a challenging task. The critical issue is to optimize the network structure to improve network capacity and avoid traffic congestion. We are interested in taking user's routes such that it is least congested with optimal network capacity. Network capacity may be improved either by optimizing network topology or enhancing in routing approach. In this context, we propose and design a model of the time varying data communication networks (TVCN) based on the dynamics of in-flowing links. Newly appeared node prefers to attach with most influential node present in the network. In this paper, influence is termed as \textit{reputation} and is applied for computing overall congestion at any node. User path with least betweenness centrality and most reputation is preferred for routing. Kelly's optimization formulation for a rate allocation problem is used for obtaining optimal rates of distinct users at different time instants and it is found that the user's path with lowest betweenness centrality and highest reputation will always give maximum rate at stable point.