{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T08:38:14Z","timestamp":1773218294972,"version":"3.50.1"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T00:00:00Z","timestamp":1707350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"National Education Examination Research Project","award":["GJK2021028"],"award-info":[{"award-number":["GJK2021028"]}]},{"name":"Humanities and Social Sciences Research Key Project of Chongqing Municipal Education Commission","award":["23SKGH247"],"award-info":[{"award-number":["23SKGH247"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The problem of detecting communities in real-world networks has been extensively studied in the past, but most of the existing approaches work on single-domain networks, i.e. they consider only one type of relationship between nodes. Single-domain networks may contain noisy edges and they may lack some important information. Thus, some authors have proposed to consider the multiple relationships that connect the nodes of a network, thus obtaining multi-domain networks. However, most community detection approaches are limited to multi-layer networks, i.e. networks generated from the superposition of several single-domain networks (called layers) that are regarded as independent of each other. In addition to being computationally expensive, multi-layer approaches might yield inaccurate results because they ignore potential dependencies between layers. This paper proposes a multi-domain discrete-time quantum walks (MDQW) model for multi-domain networks. First, the walking space of network nodes in multi-domain network is constructed. Second, the quantum permutation circuit of the coin state is designed based on the coded particle state. Then, using different coin states, the shift operator performs several quantum walks on the particles. Finally, the corresponding update rule is selected to move the node according to the measurement result of the quantum state. With continuous update iteration, the shift operator automatically optimizes the discovered community structure. We experimentally compared our MDQW method with four state-of-the-art competitors on five real datasets. We used the normalized mutual information (NMI) to compare clustering quality, and we report an increase in NMI of up to 3.51 of our MDQW method in comparison with the second-best performing competitor. The MDQW method is much faster than its competitors, allowing us to conclude that MDQW is a useful tool in the analysis of large real-life multi-domain networks. Finally, we illustrate the usefulness of our approach on two real-world case studies.<\/jats:p>","DOI":"10.1093\/comjnl\/bxae013","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T12:26:02Z","timestamp":1707481562000},"page":"2379-2389","source":"Crossref","is-referenced-by-count":2,"title":["Discrete-Time Quantum Walks Community Detection in Multi-Domain Networks"],"prefix":"10.1093","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8619-0356","authenticated-orcid":false,"given":"Xiaoyang","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"},{"name":"Chongqing University of Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8941-6103","authenticated-orcid":false,"given":"Nan","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"},{"name":"Chongqing University of Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9601-1550","authenticated-orcid":false,"given":"Yudie","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"},{"name":"Chongqing University of Technology , School of Computer Science and Engineering, , N0.69 Hongguang Road, Banan District, Chongqing 400054 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1528-7203","authenticated-orcid":false,"given":"Giacomo","family":"Fiumara","sequence":"additional","affiliation":[{"name":"Department of Mathematical, University of Messina , V.le F. Stagno D\u2019Alcontres, 31, 98166 Messina , Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7421-216X","authenticated-orcid":false,"given":"Pasquale","family":"De Meo","sequence":"additional","affiliation":[{"name":"Department of Ancient and Modern Civilizations, University of Messina, Physics and Earth Sciencesviale Ferdinando Stagno d\u2019Alcontres , 98166 Messina , Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,2,8]]},"reference":[{"key":"2024062414154179800_ref1","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/978-3-319-68179-5_53","volume-title":"Ubiquitous Networking-Third International Symposium","author":"Mourchid","year":"2017"},{"key":"2024062414154179800_ref2","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1137\/18M1231304","article-title":"Relating modularity maximization and stochastic block models in multilayer networks","volume":"1","author":"Pamfil","year":"2019","journal-title":"SIAM J Math Data Sci"},{"key":"2024062414154179800_ref3","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1137\/1.9781611975673.43","volume-title":"SIAM International Conference on Data Mining (SDM19)","author":"Veldt","year":"2019"},{"key":"2024062414154179800_ref4","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1145\/3336191.3371806","volume-title":"The International Conference on Web Search and Data Mining","author":"Luo","year":"2020"},{"key":"2024062414154179800_ref5","doi-asserted-by":"crossref","first-page":"118737","DOI":"10.1016\/j.eswa.2022.118737","article-title":"Link prediction approach combined graph neural network with capsule network","volume":"212","author":"Liu","year":"2023","journal-title":"Expert Syst Appl"},{"key":"2024062414154179800_ref6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-031-01874-9","volume-title":"Community Search over Big Graphs. 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