The Bond-Electron Matrix

The bond-electron matrices BE of Ugi and coworkers (Dugundji and Ugi, 1973 Ugi et al., 1979,1990) represent a variant of the atom-bond matrices. They are defined as 

It should be noted that the sum of the elements in the i-th row or column of a BE matrix gives the number of valence electrons of atom i  

This transformation can be described by means of the following equation  

the symbols BE(A,) and BE(A2) stand for the bond-electron matrices of reactants Aj and products A2, and RM symbolizes the reaction matrix, respectively. The off-diagonal entries of the reaction matrix (RM)ij, 

---

In the adjacency matrix, no bonds are considered. This would be possible by the analogous representation of a molecule based on the bond electron matrix, or BE matrix for short. In the latter, the -fold connection of two nodes as well as the number of n free electrons of an atom is accounted for. 

Structure 1 is represented by a BE-matrix (the bond-electron matrix of structure 1, i.c., of the [ensemble of] reactants). Structure 2, i.e. the [ensemble of] products, is represented by a BE-matrix B. Such a transition is commonly called a reaction. The fundamental equation of the Dugundji-Ugi-model is ... 

---