Graph-theoretical interpretation of Ugi's concept of the reaction network

The concept of a reaction network, initially suggested by Ugi and coworkers, in the framework of the graph-theoretical model of organic chemistry is elaborated. The reaction network for a pair of isomeric educt molecular (G _E) and product molecular graphs (G _P) is determined as an oriented graph. Its edge, beginning at a graph-vertexG _i –1 and ending at a graph-vertexG _i , corresponds to a feasible transformation (chemical reaction) constrained by a condition of descending chemical distance from the product graphG _P, i.e.CD(G _i –1,G _P) >CD(G _i ,G _P). In the reaction network, an oriented path which begins at G_E and ends atG _P corresponds to the decomposition of the overall transformationG _E G _P into a sequence of elementary transformationsG ₀ =G _E G ₁ G ₂ ... G _i–1 G _i =G _P that may be assigned to intermediates of the overall transformation.