Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman- Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks. PACS number: 89.75 Submitted to: J. Phys. A: Math. Gen. ‡ Author to whom,any correspondence should be addressed Motif-based communities in complex networks,2

Extended reduced graphs provide summary representations of chemical structures using pharmacophore-type node descriptions to encode the relevant molecular properties. Commonly used similarity measures using reduced graphs convert these graphs into 2D vectors like fingerprints, before chemical comparisons are made. This study investigates the effectiveness of a graph-only driven molecular comparison by using extended reduced graphs along with graph edit distance methods for molecular similarity calculation as a tool for ligand-based virtual screening applications, which estimate the bioactivity of a chemical on the basis of the bioactivity of similar compounds. The results proved to be very stable and the graph editing distance method performed better than other methods previously used on reduced graphs. This is exemplified with six publicly available data sets: DUD-E, MUV, GLL&GDD, CAPST, NRLiSt BDB, and ULS-UDS. The screening and statistical tools available on the ligand-based virtual screening benchmarking platform and the RDKit were also used. In the experiments, our method performed better than other molecular similarity methods which use array representations in most cases. Overall, it is shown that extended reduced graphs along with graph edit distance is a combination of methods that has numerous applications and can identify bioactivity similarities in a structurally diverse group of molecules.