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Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be \u201cphantom alignment strength\u201d from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The <jats:italic>Phantom Alignment Strength Conjecture<\/jats:italic> introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.<\/jats:p>","DOI":"10.1007\/s41109-021-00398-z","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":5,"title":["The phantom alignment strength conjecture: practical use of graph matching alignment strength to indicate a meaningful graph match"],"prefix":"10.1007","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3604-6652","authenticated-orcid":false,"given":"Donniell E.","family":"Fishkind","sequence":"first","affiliation":[]},{"given":"Felix","family":"Parker","sequence":"additional","affiliation":[]},{"given":"Hamilton","family":"Sawczuk","sequence":"additional","affiliation":[]},{"given":"Lingyao","family":"Meng","sequence":"additional","affiliation":[]},{"given":"Eric","family":"Bridgeford","sequence":"additional","affiliation":[]},{"given":"Avanti","family":"Athreya","sequence":"additional","affiliation":[]},{"given":"Carey","family":"Priebe","sequence":"additional","affiliation":[]},{"given":"Vince","family":"Lyzinski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"issue":"2","key":"398_CR1","doi-asserted-by":"publisher","first-page":"1005989","DOI":"10.1371\/journal.pcbi.1005989","volume":"14","author":"A Arnatkevic\u0306i\u016bt\u0117","year":"2018","unstructured":"Arnatkevic\u0306i\u016bt\u0117 A, Fulcher BD, Pocock R, Fornito A (2018) Hub connectivity, neuronal diversity, and gene expression in the Caenorhabditis elegans connectome. 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