Let us represent molecules by graphs (atoms are vertices and bonds are edges). Let $A$ be the adjacency matrix of the molecular graph. $A_{ij} = b$ where $b$ is either binary: 0 when atom i and j are not bonded else 1 (Repr. 1). Or, further we may take b from the set $\{0,1,2,3\}$ depending on whether the no bond (0) or single(1) double(2) or triple (3) bond is present (Rper. 2). Here were are not distinguishing the atoms - for our purose they represent a node in a graph.
Let us consider only non-isomers and molecules with at least 10 atoms. How different will be two molecules with same graphs (with respect to Repr. 1 or Repr. 2) in terms of their properties or particularly about drug-like properties. My interest is to know how faithfully the topological indices characterizes the molecular activity. Specific or general examples of pairs of non-isomer molecules with same graph but very different property could be useful. It would be helpful if I can find enough examples to convince myself about the usefulness or otherwise of topological indices which are calculated from the grpahical representation outlined above. Topological indices are popular in drug discovery research, but I am not very much convinced about their utility since most the results published are not statistically significant (use of very small data size - from 15 to some hundreds molecules, among other weakness) nor rigorously validated.
Thank you.