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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 \u201cstructural signatures\u201d within different genres of graph. Similarities also emerge between our findings and those in other disciplines, such as the preponderance of transitive triads.<\/jats:p>","DOI":"10.1007\/s41109-021-00403-5","type":"journal-article","created":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T09:02:52Z","timestamp":1630141372000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Dyads, triads, and tetrads: a multivariate simulation approach to uncovering network motifs in social graphs"],"prefix":"10.1007","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4211-0489","authenticated-orcid":false,"given":"Diane","family":"Felmlee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cassie","family":"McMillan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger","family":"Whitaker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"key":"403_CR1","unstructured":"Almquist ZW (2014) networkdata: Lin Freeman\u2019s network data collection. 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This research was approved by the Pennsylvania State University IRB (STUDY00008769; STUDY00008773).","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"The authors declare that they have no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"63"}}