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

Felmlee, Diane, McMillan, Cassie and Whitaker, Roger ORCID: https://orcid.org/0000-0002-8473-1913 2021. Dyads, triads, and tetrads: a multivariate simulation approach to uncovering network motifs in social graphs. Applied Network Science 6 (1) , 63. 10.1007/s41109-021-00403-5

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics Crime and Security Research Institute (CSURI)
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publisher:	SpringerOpen
ISSN:	2364-8228
Funders:	Dstl
Date of First Compliant Deposit:	20 September 2021
Date of Acceptance:	26 July 2021
Last Modified:	03 May 2023 20:39
URI:	https://orca.cardiff.ac.uk/id/eprint/144290

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