A worked toy network showing enumeration of EFMs. (A) Toy network with 14 reactions, 8 internal metabolites, and DoF of 6. (B) The network has 9 EFMs, sequentially enumerated from left to right by the depth-first search algorithm. Shaded zeros are the leading DoF-1 IFF for the EFMs. The arrow between a pair of EFM columns (i and i + 1) denotes the conversion of EFM
’s most terminal IFF to FAF before EFM
can be found. The set of IFF is unique for each EFM when only the leading reactions are chosen as pivot rows (see also Additional file 1). (C) A list of the sequence of IFF and FAF produced when searching from EFM 3 to EFM 4, and from EFM 7 to EFM 8. Indices of the IFF and FAF are shown. Full arrow indicates forward-tracking; dotted arrow indicates backtracking. Reaction indices in bold indicate successful conversion of a terminal IFF to FAF.