MOTIVATION: Next-generation sequencing techniques have facilitated a large-scale analysis of human genetic variation. Despite the advances in sequencing speed, the computational discovery of structural variants is not yet standard. It is likely that many variants have remained undiscovered in most sequenced individuals. RESULTS: Here, we present a novel internal segment size based approach, which organizes all, including concordant, reads into a read alignment graph, where max-cliques represent maximal contradiction-free groups of alignments. A novel algorithm then enumerates all max-cliques and statistically evaluates them for their potential to reflect insertions or deletions. For the first time in the literature, we compare a large range of state-of-the-art approaches using simulated Illumina reads from a fully annotated genome and present relevant performance statistics. We achieve superior performance, in particular, for deletions or insertions (indels) of length 20-100 nt. This has been previously identified as a remaining major challenge in structural variation discovery, in particular, for insert size based approaches. In this size range, we even outperform split-read aligners. We achieve competitive results also on biological data, where our method is the only one to make a substantial amount of correct predictions, which, additionally, are disjoint from those by split-read aligners. AVAILABILITY: CLEVER is open source (GPL) and available from http://clever-sv.googlecode.com. CONTACT: firstname.lastname@example.org or email@example.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.