{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:24:00Z","timestamp":1776785040921,"version":"3.51.2"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2022,3,3]],"date-time":"2022-03-03T00:00:00Z","timestamp":1646265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["1R01GM120733"],"award-info":[{"award-number":["1R01GM120733"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation [CAREER","award":["CCF-1452795"],"award-info":[{"award-number":["CCF-1452795"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,4,28]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Motivation<\/jats:title><jats:p>Prediction of node and graph labels are prominent network science tasks. Data analyzed in these tasks are sometimes related: entities represented by nodes in a higher-level (higher scale) network can themselves be modeled as networks at a lower level. We argue that systems involving such entities should be integrated with a \u2018network of networks\u2019 (NoNs) representation. Then, we ask whether entity label prediction using multi-level NoN data via our proposed approaches is more accurate than using each of single-level node and graph data alone, i.e. than traditional node label prediction on the higher-level network and graph label prediction on the lower-level networks. To obtain data, we develop the first synthetic NoN generator and construct a real biological NoN. We evaluate accuracy of considered approaches when predicting artificial labels from the synthetic NoNs and proteins\u2019 functions from the biological NoN.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>For the synthetic NoNs, our NoN approaches outperform or are as good as node- and network-level ones depending on the NoN properties. For the biological NoN, our NoN approaches outperform the single-level approaches for just under half of the protein functions, and for 30% of the functions, only our NoN approaches make meaningful predictions, while node- and network-level ones achieve random accuracy. So, NoN-based data integration is important.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>The software and data are available at https:\/\/nd.edu\/~cone\/NoNs.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/btac133","type":"journal-article","created":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T22:26:15Z","timestamp":1646087175000},"page":"2544-2553","source":"Crossref","is-referenced-by-count":51,"title":["Modeling multi-scale data via a network of networks"],"prefix":"10.1093","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4523-1262","authenticated-orcid":false,"given":"Shawn","family":"Gu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, University of Notre Dame , Notre Dame, IN 46556, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, University of Notre Dame , Notre Dame, IN 46556, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pietro Hiram","family":"Guzzi","sequence":"additional","affiliation":[{"name":"Department of Surgical and Medical Sciences, University Magna Graecia of Catanzaro , Catanzaro 88100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tijana","family":"Milenkovi\u0107","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, University of Notre Dame , Notre Dame, IN 46556, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,3,3]]},"reference":[{"key":"2023041402550242900_","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/75556","article-title":"Gene ontology: tool for the unification of biology","volume":"25","author":"Ashburner","year":"2000","journal-title":"Nat. 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