**Abstract:**
We establish several properties of the integrated density of states for
random quantum graphs: Under appropriate ergodicity and amenability assumptions,
the integrated density of states can be defined using an exhaustion procedure by
compact subgraphs. A trace per unit volume formula holds, similarly as in the
Euclidean case. Our setting includes periodic graphs. For a model where the edge lengths are random and vary independently in a smooth way we prove a Wegner estimate and related regularity results for the integrated density of states. These results are illustrated for an example based on the Kagome lattice. In the periodic case we characterise all compactly supported eigenfunctions and calculate the position and size of discontinuities of the
integrated density of states. (joint work with Daniel Lenz, Norbert Peyerimhoff and Ivan Veselic)