Cross-disciplinary detection and analysis of network motifs

The detection of network motifs has recently become an important part of network analysis across all disciplines. In this work, we detected and analyzed network motifs from undirected and directed networks of several different disciplines, including biological network, social network, ecological network, as well as other networks such as airlines, power grid, and co-purchase of political books networks. Our analysis revealed that undirected networks are similar at the basic three and four nodes, while the analysis of directed networks revealed the distinction between networks of different disciplines. The study showed that larger motifs contained the three-node motif as a subgraph. Topological analysis revealed that similar networks have similar small motifs, but as the motif size increases, differences arise. Pearson correlation coefficient showed strong positive relationship between some undirected networks but inverse relationship between some directed networks. The study suggests that the three-node motif is a building block of larger motifs. It also suggests that undirected networks share similar low-level structures. Moreover, similar networks share similar small motifs, but larger motifs define the unique structure of individuals. Pearson correlation coefficient suggests that protein structure networks, dolphin social network, and co-authorships in network science belong to a superfamily. In addition, yeast protein-protein interaction network, primary school contact network, Zachary's karate club network, and co-purchase of political books network can be classified into a superfamily.