We get : no. of complexes – no. of species = no. of connected components – no. of conservation laws. ]]>

So, in deficiency 0 networks the number of connected components is equal to the number of conservation laws. Is this correct?

Let’s see. The deficiency is the number of complexes minus the number of connected components minus the dimension of the stochiometric subspace. So, if it’s zero,

• The number of complexes equals the number of connected components plus the dimension of the stochiometric subspace.

On the other hand,

• The number of linear conservation laws is the number of species minus the dimension of the stoichiometric subspace.

Putting these equations together, I can get an equation involving the number of connected components and the number of conservation laws. But it doesn’t seem to be the equation you suggest! What equation do we actually get?

]]>Given your interest in leaves over hypercubes (e.g., 1st network th post), perhaps the Belousov–Zhabotinsky reaction would stimulate some ideas? It is an example of a class of reactions that under certain circumstances, exhibit fundamental self organizing properties (like leaves!).

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