Consider a huge network of possibly unknown size but known structure. To model this situation, we may take an infinite graph and equip it with the appropriate combinatorial assumptions. Along the edges of the network some transport processes take place that are coupled in the vertices in which the edges meet. This means that we consider each edge as an interval and describe functions on it, that is, we consider a metric graph. Such systems of partial differential equations on a metric graph are also known as quantum graphs. The transport processes (or flows) on the edges are given by partial differential equations of the form \(\frac{\partial }{\partial t}u_j(t,x)= c_j \frac{\partial }{\partial x}u_j(t,x)\) and are interlinked in the common nodes via some prescribed transmission conditions.