Abstract
Motifs represent local subgraphs that are overrepresented in networks. Several disciplines document multiple instances in which motifs appear in graphs and provide insight into the structure and processes of these networks. In the current paper, we focus on social networks and examine the prevalence of dyad, triad, and symmetric tetrad motifs among 24 networks that represent six types of social interactions: friendship, legislative co-sponsorship, Twitter messages, advice seeking, email communication, and terrorist collusion. Given that the correct control distribution for detecting motifs is a matter of continuous debate, we propose a novel approach that compares the local patterns of observed networks to random graphs simulated from exponential random graph models. Our proposed technique can produce conditional distributions that control for multiple, lower-level structural patterns simultaneously. We find evidence for five motifs using our approach, including the reciprocated dyad, three triads, and one symmetric tetrad. Results highlight the importance of mutuality, hierarchy, and clustering across multiple social interactions, and provide evidence of “structural signatures” within different genres of graph. Similarities also emerge between our findings and those in other disciplines, such as the preponderance of transitive triads.
Highlights
Complex networks that arise in nature, such as those from biochemistry, neurobiology, ecology, and engineering, exhibit some of the same, simple structures that occur with greater than expected frequency, known as “network motifs” (Milo et al 2002)
To identify overrepresented directed triads, we estimate a second set of exponential random graph models (ERGMs) on each of the directed networks in our sample that generate random graphs that are identical to those that condition on the dyad distribution of the observed network
Certain motifs emerge in our graphs that are common in various disciplines, such as the four-clique, which predominates in graphs of protein structures and electrical power grids (e.g., Milo et al 2004)
Summary
Complex networks that arise in nature, such as those from biochemistry, neurobiology, ecology, and engineering, exhibit some of the same, simple structures that occur with greater than expected frequency, known as “network motifs” (Milo et al 2002). The purpose of this research, is to examine motifs within multiple types of social networks, and focus on the relative frequency of two, three, and four node subgraphs, known as dyads, triads, and tetrads, respectively. Research in the natural and physical sciences often compares the patterns of local structures to random networks that are conditional on observed degree distributions (e.g., Kashtan and Alon 2005; Shenn-Orr et al 2002; Yeger-Lotem et al 2004).
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