{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T00:14:05Z","timestamp":1782951245737,"version":"3.54.5"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T00:00:00Z","timestamp":1666915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deputyship for Research and Innovation of the Saudi Ministry of Education","award":["If-PSAU-2021\/01\/18316"],"award-info":[{"award-number":["If-PSAU-2021\/01\/18316"]}]},{"name":"PSAU Advanced Computational Intelligent Systems Engineering (ACIISE) Research Group","award":["If-PSAU-2021\/01\/18316"],"award-info":[{"award-number":["If-PSAU-2021\/01\/18316"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Prediction of missing links is an important part of many applications, such as friends\u2019 recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein\u2013protein networks.<\/jats:p>","DOI":"10.3390\/e24111547","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T04:57:34Z","timestamp":1667105854000},"page":"1547","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Simplified Quantum Walk Model for Predicting Missing Links of Complex Networks"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1938-0149","authenticated-orcid":false,"given":"Wen","family":"Liang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8532-1978","authenticated-orcid":false,"given":"Fei","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4964-6609","authenticated-orcid":false,"given":"Abdullah M.","family":"Iliyasu","sequence":"additional","affiliation":[{"name":"College of Engineering, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"School of Computing, Tokyo Institute of Technology, Yokohama 226-8502, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1066-8261","authenticated-orcid":false,"given":"Ahmed S.","family":"Salama","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Technology, Future University in Egypt, Cairo 11835, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaoru","family":"Hirota","sequence":"additional","affiliation":[{"name":"School of Computing, Tokyo Institute of Technology, Yokohama 226-8502, Japan"},{"name":"School of Automation, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/TKDE.2020.2997861","article-title":"Cross-network Skip-gram embedding for joint network alignment and link prediction","volume":"34","author":"Du","year":"2022","journal-title":"IEEE Trans. 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