Deciphering the Transport in complex systems

In the past few years have studied the topological structure of static and evolving complex networks. In more recent times, researchers have become interested in analyzing the network as a dynamical system on which there is a dynamical quantity that varies in time, or where packets are transported across the network. We discuss examples of transport over complex networks that can involve the generation of spontaneous magnetization or nontrivial topological phase transitions in magnetic systems; the propagation of electric or spin currents, quantum information, photons; the evolution of stress dissipation in active geophysical regions; transport of vehicles in cities or packets in communication networks, etc. We also present recent simulation and analytical results on the transport of a classical quantity in a generalization of the “Ehrenfest urn” over complex networks.