Graph codes and a definition of structural similarity

Abstract

A succinct linear notation system to encode the structure of a graph is exemplified. The notation requires a prior canonical numbering of the graph nodes based on the lengths of a longest path and path branches, and uses locants to designate branch positions and cyclicity. An algorithm and computer program to obtain the longest paths and a spanning tree containing a longest path is described. An index which measures the similarity of a pair of graphs is defined based on a comparison of their linear codes.