Transport Problems in Networks

Consider a closed network of pipes or wires in which some material (water, electrons, information packets, goods, etc.) is flowing at constant speed on each edge, with no friction or loss. In the nodes of the network the material is redistributed into the pipes according to Kirchhoff’s laws. Simplifying the physical laws and concentrating on the structure of the network, this situation can be described by a system of linear transport equations on the edges of a graph.