Let us briefly recall our definition of recyclization graphs. We call recyclization (or ring transformation) any transformation of a heterocycle, that include the steps of ring opening and ring closure in any sequence. We shall consider mainly monocyclic systems, and among condensed heterocycles - only those containing one joint bond between the annelated rings (as it is in indole or acridine). Let us call ring transformation to be simple ring transformation (or SRT) if:
(a) there is no formation of any transient cycles via recyclization, except the final one;
(b) there is no permutation of atoms or groups via ring transformation;
(c) the initial cycle is transformed into no more than one cycle of the final structure.

Most of known recyclizations are SRTs, particularly, the large family of ANRORC-reactions. (Boundaries of the term are discussed early [3,4]. Below we shall be limited only by SRTs. The main idea of our approach is rather simple. Since the mechanism of a recyclization is established, the skeleton of the initial cycle can be easily found among the atoms and bonds of final products and vice versa, the skeleton of the final cycle can be found among the atoms and bonds of the starting reagents. Paying all the attention only to these cyclic skeletal substructures (and ignoring all other details of molecular structure), we can get significant simplification of the chemical equation. The reaction mechanism establishes the correspondence between matching atoms and bonds of the initial and final cycles. Therefore, just these cyclic (initial and final) substructures can be chosen for superposition to define the graph of ring transformation reaction.

Let us give more strict definitions following Ref. 3. Let us define for any SRT (with the mechanism known beforehand) two types of graphs - the molecular graphs (that are not coincide with initial and final structures and are determined only by the given type of transformation) and the recyclization graph (for any reaction that is SRT). Let us define the molecular graph M_s of starting reagents as the set of vertices and edges, that correspond only to those V atoms and R_s skeletal bonds that either exist in the initial cycle or are incorporated in the final cycle. By analogous manner, the molecular graph of final products M_f (with V vertices and R_f edges) contains the same V atoms and only those skeletal bonds, that either exist in the final cycle or were presented in the initial cycle. Let us keep the symbols of heteroatoms as the labels of vertices in the graphs M_s and M_f and omit all other symbols (like hydrogen atoms, multiple bonds, and any substituents including annelated rings). Although the same V vertices are chosen to construct both graphs M_s and M_f , the number and/or distribution of edges in these graphs is obviously different. Let us enumerate the vertices of M_s -graph; then the mechanism of SRT immediately permits us to enumerate by corresponding numbers the matching vertices of the M_f -graph. Let us make mental superposition of the structures of graphs M_s and M_f according to the matching vertices (and edges) with identical numbers. The pairs of vertices with the same number should be identified into one new vertex, as well as the pairs of edges - into one new edge. Let us define such superposition as the new recyclization graph with V vertices. Let us designate the edges of recyclization graph (presented also in the graphs M_s and/or in M_f ) by the following manner:
(a) by the dashed line (edge) if the edge is presented only in one (but not another) M-graphs;
(b) by the bold line if the edge belongs to both (initial and final) cycles;
(c) by the usual (solid) line if the edge belongs to only one cycle of M-graphs.
Click here to see an example.