On Motifs and Functional Blocks in Complex Networks

This article addresses the presence and size of basic functional modules (motifs) in complex systems. The current view of motifs is that they are small modules of 3-4 “nodes”, which occur significantly more frequently in real-world networks than expected by chance alone. We show that standard functional blocks used to build real-world circuits where a node is interpreted as a primitive component, such as a primitive logic gate (AND, NAND, OR, NOR and NOT etc.), are much larger than the proposed 3-4 node motifs. In fact, these functional blocks themselves are typically comprised of a collections of several 3-4 node motifs. Further, we show that random-graph models currently cannot generate sub-graphs with the topology of functional blocks, implying that these functional blocks cannot be defined using the notions of statistical over-representation used for motifs. We argue that, for this domain, the statistical over-representation of 3-4 node motifs is due to functional blocks consisting of motif-clusters, and not that motifs, in and of themselves, play a significant functional role in a circuit.