Information theory concepts and methodologies constitute the background of how communication systems are studied and understood. They are focused mainly on the source-channel-receiver problem and on the asymptotic limits of accuracy and communication rates, which are the classical problems studied by Shannon. However, the impact of information theory on networks (acting as the channel) is just starting. Here, we present an approach to understand how information flows in any connected network. Our approach is based on defining linear conservative flows that travel through the network from single or multiple sources to receivers. With these flows, we define a transition probability matrix that is similar to a Markovian process. Consequently, this framework allows us to have an analytical description of the problem and also to link the topological invariants of the network, such as the node degree, with the information flow and capacity, namely, the maximum amount of information generated by the network for any source-receiver configuration. In particular, our approach is able to deal with information transmission in modular networks (networks containing community structures) or multiplex networks (networks with multiple layers), which are nowadays of paramount importance.

PACS Nos 89.75.Hc; 45.30.+s; 02.50.-r; 41.20-q