Dyads, triads, and tetrads: a multivariate simulation approach to uncovering network motifs in social graphs

Abstract Motifs represent local subgraphs that are overrepresented in networks. Several disciplines document multiple instances which motifs appear graphs and provide insight into the structure processes of these In current paper, we focus on social networks examine prevalence dyad, triad, symmetric tetrad among 24 six types interactions: friendship, legislative co-sponsorship, Twitter messages, advice seeking, email communication, terrorist collusion. Given correct control distribution for detecting is a matter continuous debate, propose novel approach compares patterns observed to random simulated from exponential graph models. Our proposed technique can produce conditional distributions multiple, lower-level structural simultaneously. We find evidence five using our approach, including reciprocated three triads, one tetrad. Results highlight importance mutuality, hierarchy, clustering across interactions, “structural signatures” within different genres graph. Similarities also emerge between findings those other disciplines, such as preponderance transitive triads.