I am new in metabolic network analysis and elementary flux mode (EFM) concept. I just started reading the main paper in this field that dates back to 1994, entitled "On elementary flux modes in biochemical reaction systems at steady-state."

In page 177, there is a matrix which the right-hand part of it shows stoichiometry matrix for reaction network in figure 2.

I have two questions about it:

1) How can we determine the sign of value in stoichiometry matrix for bidirectional edges, e.g. reaction V4, V5, and V6? As you can see, the position of [6,7] and [6,9] are -1 and 1 respectively. Can we assign them as [6,7] =1 and [6,9] =-1?

2) How matrix T^(1) is determined according to T^(0)? I do know there are 5 lines of explanations on page 177, however, I can't understand it. I really need someone to help me to understand it.

Thanks for your kind help.