The Feinberg Approach to Network Topology

Feinberg bases his approach on the concept of complex, which is originally due (in its explicit form) to Horn and Jackson (1972), and which can be traced back in a more implicit form to the work of Krambeck (1970). Complexes are groupings of components that can appear in any given reaction for instance, in the (molar-based described) reaction 

A] and A2 + A3 are complexes. Let N be the total number of complexes in any given reaction network. 

Finally, Feinberg considers the rank of the stoichiometric matrix, R. He then defines a deficiency of the reaction network, 5,as6 = N — N — R. In his series of papers, Feinberg obtains a number of strong results for systems of deficiency 0 and deficiency 1 these are not discussed here, and only very concisely in the next section. For the whole strength of the theory the reader is referred to the original Feinberg papers. 

Feinberg also keeps track of how the arrows connecting any two complexes in a linkage class are oriented for instance, the case of the three xylene isomers could be regarded as A B C A, or as A - B C A, or any other in- 

However, consider the case where one allows for any two olefins to react with each other, say, with / and J, the carbon numbers of generic olefins  

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Appendix C The Feinberg Approach to Network Topology Appendix D Mathematical Concepts References... 

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