These reaction templates were then classified in terms of the topology of the reaction center, detailed in Table . The most relevant topological feature for our purposes is the cycle structure. We made use of the well-known fact that every graph can be decomposed in 2-connected components (where any two vertices are located on a common cycle), and a tree-like remainder that may in turn consist of several mutually disconnected parts. Each of the 2-connected components can be represented by a minimal cycles basis (MCB). Even though the MCB of a graph is not unique in general, it can be shown that all MCBs have the same number of cycles with the same length. 40,41 Thus we could characterize the reaction center by the list of cycle lengths of any of its MCBs, augmented by a zero for every tree-like component. To obtain a uniquely defined descriptor, we stipulated the list of cycle lengths is sorted in ascending order.