  In this paper, we introduce a codification of the paths towards
synchronization for synchronizing flows defined over a network. The collection
of paths toward synchronization defines a combinatorial structure: the
transition diagram. We describe the transition diagram corresponding to the
Laplacian flow over the completely connected graph. This applies to the
Kuramoto flow over the same graph when initial conditions close to the diagonal
are considered. We present as well some results concerning the Laplacian and
Kuramoto flows over the complete bipartite graph.
