Cellular networks in a broad variety of materials influence many materials properties—a particularly important subject when it comes to microstructural coarsening of these networks. Hence, changes in the networks are of intense scientific and technological interest, where all topological changes occur in form of topological transitions. In two dimensions, there are three types of transitions, namely grain disappearance events, neighbour switching events, and edge disappearance events. Each event changes not only the morphology of a grain but also the local topology around this grain. The present work is the first investigation aimed at the question whether such topological transitions describe a topological random walk for individual grains or if they are a pure geometric necessity for structural space filling.