Enrichment and aggregation of topological motifs are independent organizational principles of integrated interaction networks

Topological network motifs represent functional relationships within and between regulatory and protein-protein interaction networks. Enriched motifs often aggregate into self-contained units forming functional modules. Theoretical models for network evolution by duplication-divergence mechanisms and for network topology by hierarchical scale-free networks have suggested a one-to-one relation between network motif enrichment and aggregation, but this relation has never been tested quantitatively in real biological interaction networks. Here we introduce a novel method for assessing the statistical significance of network motif aggregation and for identifying clusters of overlapping network motifs. Using an integrated network of transcriptional, posttranslational and protein-protein interactions in yeast we show that network motif aggregation reflects a local modularity property which is independent of network motif enrichment. In particular our method identified novel functional network themes for a set of motifs which are not enriched yet aggregate significantly and challenges the conventional view that network motif enrichment is the most basic organizational principle of complex networks.