First-order and N-order reaction overlaps. This picture presents the two possible ways in which two species-sets can be connected: directly, by means of reactions such as R1 and R2, for instance, or indirectly, like for R*, which represents the fact that in order to move from species-set X to species-set Y, one or more additional species-sets have to be traversed. These concepts are used in the N-order reachability (duplicate reaction detection) among species-sets, which builds a reaction composition analysis by constructing a matrix which abstracts the overall species-set connectivity.
Umeton et al. BMC Bioinformatics 2012 13(Suppl 4):S6 doi:10.1186/1471-2105-13-S4-S6