The requirement of aligning each individual molecule in a data set severely limits the type of molecules which can be analysed with traditional structure activity relationship (SAR) methods. A method which solves this problem by using relations between objects is inductive logic programming (ILP). Another advantage of this methodology is its ability to include background knowledge as 1st-order logic. However, previous molecular ILP representations have not been effective in describing the electronic structure of molecules. We present a more unified and comprehensive representation based on Richard Bader's quantum topological atoms in molecules (AIM) theory where critical points in the electron density are connected through a network. AIM theory provides a wealth of chemical information about individual atoms and their bond connections enabling a more flexible and chemically relevant representation. To obtain even more relevant rules with higher coverage, we apply manual postprocessing and interpretation of ILP rules. We have tested the usefulness of the new representation in SAR modelling on classifying compounds of low/high mutagenicity and on a set of factor Xa inhibitors of high and low affinity.