In this paper, we present a running influence model for evaluating the pairwise impact between communities in citation networks and define the time limitations of the model. The model improves a recent one from the literature. To compare and contrast different communities influence, we present a metric for estimating the overall running influence value of particular community. We also study the problem of the time dependency of the influence within citation networks. To conduct the community influence analysis, we perform the experiments using a real-world database. The results are compared to both real-world ranking and the state-of-the-art method. They show the adequacy of the proposed metrics and model of running influence. We also demonstrate the importance of proposed differentiation within calculation and interpretation of the influence in time-dependent citation networks