Recurrent Structural Motifs Reflect Characteristics of Distinct Networks

In large-scale networks, certain topological patterns may occur more frequently than expected from a null model that preserves global (such as the density of the graph) and local (such as the connectivity of each node) properties of the graph. These network motifs are the building blocks of large-scale networks and may confer functional/mechanistic implications of their underlying processes. Despite active investigations and rich literature in systems biology, network motifs are less explored in social network studies. In this work, we modified and improved the method from Milo et al. 2002 to detect significantly enriched motifs in both directed and undirected networks. We applied this method to identify 3-node and 4-node motifs from the datasets of 18 networks (4 directed and 14 undirected) covering social interactions, co-authorships, web document hyperlinks, neuronal circuitry, protein-protein interactions (PPI), trophic relations in a food web, and others. Presence and absence of enriched motifs provide rich information regarding each type of network relations. In undirected networks, triangles are enriched in almost all datasets, suggesting the prevalence of transitivity in diverse networks. However, 4-node structures lacking transitivity -- diamonds and stars -- are also enriched in the majority of undirected networks. In directed networks, variations of feed-forward loops are over-represented in the networks of web document and political web log hyperlinks as well as neuronal connections. In contrast, the food web is enriched with unidirectional motifs with distinct trophic levels. These results reveal the nature of distinct types of networks and invite further explorations on the relations of network structures and types of relations.