The extant work on network analyses has thus far paid little attention to the heterogeneity in time lags and speed of information propagation along edges. In this paper, we study this novel problem, modeling the time dimension and lags on network edges, in the context of paper and patent citation networks where the variation in the speed of knowledge flows between connected nodes is apparent. We propose to model time lags in knowledge diffusions in citation networks in one of the two ways: deterministic lags and probabilistic lags. Then, we discuss two approaches of computationally working with time lags in edges of citation networks. Experimentally, we study two different applications to demonstrate the importance of the time dimension and lags in citations: (1) HITS algorithm and (2) patent citation recommendation. We conduct experiments on millions of U.S. patent data and Web of Science (WOS) paper data. Our experiments show that incorporating time dimension and lags in edges significantly improve network modeling and analyses.