From a full connectivity matrix, many of the other descriptions found to be useful for predicting relevant catalytic properties arise. This includes coordination numbers, generalized coordination, 14 site dependent scaling, and any other form of convolution which depends on connectivity information. By systematically generating these graphs, the surface atoms, adsorption atoms, and slab layering information is also made available allowing these properties to be generated automatically without use of system dependent classification techniques. By extending the connectivity matrix to include an arbitrary molecular graph, any adsorbate which can be uniquely represented as a graph can be quickly enumerated with this representation, so long as it only bonds at one single active site. It is important to note that this technique will not correctly account for stereoisomers of adsorbates on the surface. This is a well known problem and an ongoing area of research in the field of cheminformatics. A complete methodology for stereoisomer enumeration is beyond the scope of this work, however, strategies for beginning to address this issue are discussed further below.