Understanding Information Transmission in Complex Networks

Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused 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 complex network. Our approach is based on defining linear conservative flows that travel through the network from source to receiver. This framework allows us to have an analytical description of the problem and also linking the topological invariants of the network, such as the node degree, with the information flow. 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.