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Netw. Anal. Min."],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Efficiency of a system network often relies on high connectivity. However, strongly connected networks are vulnerable in a case of a spreading virus. In our study, we propose a clustering method which balances the two opposing factors: maintains a high system efficiency yet minimises the spreading potential. Our Deep Epidemic Efficiency Network (DEEN) model leverages Graph Convolutional Neural Networks and a novel loss function. In an unsupervised setting, we seek a partition that maximises the system utility while restraining the transmission rate to a desired level. We show that proposed method successfully solves three real-life problems: ride-pooling service in New York City, economic exchange between regions in Poland, and information sharing via peer-to-peer network. In particular, by dividing 150 New York taxi travellers into four groups our method increases epidemic threshold more than twofold at the cost of reducing utility only by\n                    <jats:inline-formula>\n                      <jats:tex-math>$$13\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . The model can be instrumental in future pandemic outbreaks when we need to balance between efficiency and potential spread of a virus.\n                  <\/jats:p>","DOI":"10.1007\/s13278-025-01523-x","type":"journal-article","created":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T13:06:31Z","timestamp":1765458391000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimising network efficiency in an epidemic scenario"],"prefix":"10.1007","volume":"16","author":[{"given":"Magdalena","family":"Proszewska","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Bujak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafal","family":"Kucharski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacek","family":"Tabor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marek","family":"Smieja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,11]]},"reference":[{"issue":"3","key":"1523_CR1","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1073\/pnas.1611675114","volume":"114","author":"J Alonso-Mora","year":"2017","unstructured":"Alonso-Mora J, Samaranayake S, Wallar A, Frazzoli E, Rus D (2017) On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment. 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