Topological motifs populate complex networks through grouped attachment

Network motifs are topological subgraph patterns that recur with statistical significance in a network. Network motifs have been widely utilized to represent important topological features for analyzing the functional properties of complex networks. While recent studies have shown the importance of network motifs, existing network models are not capable of reproducing real-world topological properties of network motifs, such as the frequency of network motifs and relative graphlet frequency distances. Here, we propose a new network measure and a new network model to reconstruct real-world network topologies, by incorporating our Grouped Attachment algorithm to generate networks in which closely related nodes have similar edge connections. We applied the proposed model to real-world complex networks, and the resulting constructed networks more closely reflected real-world network motif properties than did the existing models that we tested: the Erdös-Rényi, small-world, scale-free, popularity-similarity-optimization, and nonuniform popularity-similarity-optimization models. Furthermore, we adapted the preferential attachment algorithm to our model to gain scale-free properties while preserving motif properties. Our findings show that grouped attachment is one possible mechanism to reproduce network motif recurrence in real-world complex networks.