Permanence of sparse catalytic networks

Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every directed graph with a Hamiltonian circuit there is a choice of rate constants such that the system is permanent. On the other hand, one can find properties of the graphs, for example, reducibility or the presence of endpoints, that are incompatible with permanence.