A set of algorithms is presented which establish the topological identity of atoms, bonds, molecules, and ensembles of molecules from a basic connection table. The computationally inexpensive result is a fixed-length hash code which is suited for database applications and structure manipulation programs. The degree of differentiation between structural entities is adjusted easily for stereocenters, isotope labeling, atomic charges, and ionization locations or other properties. Special algorithms are presented which deal with problematic cases of uniform atomic environments. A number of practical applications demonstrate the usefulness of these hash codes. © 1994 by John Wiley & Sons, Inc.