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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.

Abstract The relationship between a firm and its supply chain has been well studied, however, the association between the position of firms in complex supply chain networks and their performance has not been adequately investigated. This is primarily due to insufficient availability of empirical data on large-scale networks. To addresses this gap in the literature, we investigate the relationship between embeddedness patterns of individual firms in a supply network and their performance using empirical data from the automotive industry. In this study, we devise three measures that characterize the embeddedness of individual firms in a supply network. These are namely: centrality, tier position, and triads. Our findings caution us that centrality impacts individual performance through a diminishing returns relationship. The second measure, tier position, allows us to investigate the concept of tiers in supply networks because we find that as networks emerge, the boundaries between tiers become unclear. Performance of suppliers degrade as they move away from the focal firm (i.e., Toyota). The final measure, triads, investigates the effect of buying and selling to firms that supply the same customer, portraying the level of competition and cooperation in a supplier’s network. We find that increased coopetition (i.e., cooperative competition) is a performance enhancer, however, excessive complexity resulting from being involved in both upstream and downstream coopetition results in diminishing performance. These original insights help understand the drivers of firm performance from a network perspective and provide a basis for further research.