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However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein\u2013protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an<jats:italic>E. coli<\/jats:italic>and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.<\/jats:p>","DOI":"10.1007\/s41109-021-00434-y","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T11:02:52Z","timestamp":1637578972000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Testing biological network motif significance with exponential random graph models"],"prefix":"10.1007","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2442-4743","authenticated-orcid":false,"given":"Alex","family":"Stivala","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Lomi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"issue":"120","key":"434_CR1","doi-asserted-by":"crossref","first-page":"20160179","DOI":"10.1098\/rsif.2016.0179","volume":"13","author":"SE Ahnert","year":"2016","unstructured":"Ahnert SE, Fink T (2016) Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space. 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