Before revision:  We explore the combinatorics of reaction networks , with a view towards the Global Attractor Conjecture. We prove that full-rank matrices with positive off-diagonal and negative diagonal entries permit a positive linear combination of the rows so that all coordinates have the same sign. Using this, we show that a reaction network has critical siphons iff it has "drainable" or "self-replicable" siphons.
After revision:  We explore the combinatorics of reaction networks , with a view towards the persistence conjecture. We introduce the notions of "drainable" or "self-replicable" siphons.