The study of biological networks and network motifs can yield significant new insights into systems biology. Previous methods of discovering network motifs ? network-centric subgraph enumeration and sampling ? have been limited to motifs of 6 to 8 nodes, revealing only the smallest network components. New methods are necessary to identify larger network sub-structures and functional motifs. Here we present a novel algorithm for discovering large network motifs that achieves these goals, based on a novel symmetry-breaking technique, which eliminates repeated isomorphism testing, leading to an exponential speed-up over previous methods. This technique is made possible by reversing the traditional network-based search at the heart of the algorithm to a motif-based search, which also eliminates the need to store all motifs of a given size and enables parallelization and scaling. Additionally, our method enables us to study the clustering properties of discovered motifs, revealing even larg...
Joshua A. Grochow, Manolis Kellis