{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:35:27Z","timestamp":1760189727209,"version":"3.37.3"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/100010052","name":"Northumbria University","doi-asserted-by":"publisher","award":["201920A1001"],"award-info":[{"award-number":["201920A1001"]}],"id":[{"id":"10.13039\/100010052","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advs. Complex Syst."],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:p> Recent theoretical studies on network robustness have focused primarily on attacks by random selection and global vision, but numerous real-life networks suffer from proximity-based breakdown. Here we introduce the multi-hop generalized core percolation on complex networks, where nodes with degree less than [Formula: see text] and their neighbors within [Formula: see text]-hop distance are removed progressively from the network. The resulting subgraph is referred to as [Formula: see text]-core, extending the recently proposed [Formula: see text]-core and classical core of a network. We develop analytical frameworks based upon generating function formalism and rate equation method, showing for instance continuous phase transition for [Formula: see text]-core and discontinuous phase transition for [Formula: see text]-core with any other combination of [Formula: see text] and [Formula: see text]. We test our theoretical results on synthetic homogeneous and heterogeneous networks, as well as on a selection of large-scale real-world networks. This unravels, e.g., a unique crossover phenomenon rooted in heterogeneous networks, which raises a caution that endeavor to promote network-level robustness could backfire when multi-hop tracing is involved. <\/jats:p>","DOI":"10.1142\/s0219525920500010","type":"journal-article","created":{"date-parts":[[2020,3,15]],"date-time":"2020-03-15T15:42:10Z","timestamp":1584286930000},"page":"2050001","source":"Crossref","is-referenced-by-count":5,"title":["MULTI-HOP GENERALIZED CORE PERCOLATION ON COMPLEX NETWORKS"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2817-3400","authenticated-orcid":false,"given":"YILUN","family":"SHANG","sequence":"first","affiliation":[{"name":"Department of Computer and Information Sciences, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,3,12]]},"reference":[{"key":"S0219525920500010BIB001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511780356"},{"key":"S0219525920500010BIB002","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199206650.001.0001"},{"key":"S0219525920500010BIB003","doi-asserted-by":"publisher","DOI":"10.1038\/35019019"},{"key":"S0219525920500010BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.022313"},{"key":"S0219525920500010BIB006","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.032820"},{"key":"S0219525920500010BIB007","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-19706-2"},{"key":"S0219525920500010BIB008","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-10063-w"},{"key":"S0219525920500010BIB009","doi-asserted-by":"publisher","DOI":"10.1145\/3199674"},{"key":"S0219525920500010BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.chb.2016.09.012"},{"key":"S0219525920500010BIB011","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-031218-013259"},{"key":"S0219525920500010BIB012","doi-asserted-by":"publisher","DOI":"10.1038\/nature08932"},{"key":"S0219525920500010BIB013","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-018-0343-1"},{"key":"S0219525920500010BIB014","first-page":"011013","volume":"7","author":"Radicchi F.","year":"2017","journal-title":"Phys. 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