Network motifs emerge from interconnections that favour stability

Abstract

The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks.