A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the proposed network-based framework paves the way not only to extending traditional information science, but also to modeling, characterizing and analyzing a broad class of real-world problems, from language communication to DNA coding. Basically, an original network is supposed to be transmitted, with or without compaction, through a sequence of symbols or time-series obtained by sampling its topology by some network dynamics, such as random walks. We show that the degree of compression is ultimately related to the ability to predict the frequency of symbols based on the topology of the original network and the adopted dynamics. The potential of the proposed approach is illustrated with respect to the efficiency of transmitting several types of topologies by using a variety of random walks. Several interesting results are obtained, including the behavior of the Barabási-Albert model oscillating between high and low performance depending on the considered dynamics, and the distinct performances obtained for two geographical models.