{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:36:42Z","timestamp":1760240202390,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91646124, 71571017, 71621001, 91746201"],"award-info":[{"award-number":["91646124, 71571017, 71621001, 91746201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2018JBM026"],"award-info":[{"award-number":["2018JBM026"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Coreness is one of the important indicators to measure the importance of a node. Traditionally, the coreness of a node is measured by k-core decomposition. However, to measure the coreness in a dynamic network, the k-core decomposition method becomes very time-consuming and inefficient, and cannot meet the need in very large real networks. Recently, the    H    operator method was proposed to calculate the coreness of a node, which provides a novel method to deal with the coreness of a node in a network. In this paper, we decode the coreness variation rule by a symmetric pair of experiments, i.e., deleting and adding edge, on real networks. Then, an algorithm to fast update the coreness of related nodes is proposed. Results on five real networks showed that the performance of the proposed algorithm was greatly enhanced and comprehensively superior to the k-core decomposition algorithm. Our study provides a promising way to optimize the algorithm of coreness calculation in the dynamic networks.<\/jats:p>","DOI":"10.3390\/sym11040477","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T03:13:42Z","timestamp":1554347622000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Coreness Variation Rule and Fast Updating Algorithm for Dynamic Networks"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4005-0339","authenticated-orcid":false,"given":"Liang","family":"Gao","sequence":"first","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ge","family":"Gao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dandan","family":"Ma","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lida","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Life Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.physa.2019.02.010","article-title":"Identifying influential spreaders based on indirect spreading in neighborhood","volume":"523","author":"Yu","year":"2019","journal-title":"Phys. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"033122","DOI":"10.1063\/1.5023736","article-title":"Scaling tunable network model to reproduce the density-driven superlinear relation","volume":"28","author":"Gao","year":"2018","journal-title":"Chaos"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.physa.2014.10.018","article-title":"Finding topological center of a geographic space via road network","volume":"419","author":"Gao","year":"2015","journal-title":"Phys. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1073\/pnas.1801545116","article-title":"Switch between critical percolation modes in city traffic dynamics","volume":"116","author":"Zeng","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, P., L\u00fc, J., and Yu, X. (2014). Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0106132"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"036104","DOI":"10.1103\/PhysRevE.65.036104","article-title":"Immunization of complex networks","volume":"65","author":"Vespignani","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_7","first-page":"12343","article-title":"Efficient immunization of populations and computers","volume":"91","author":"Cohen","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1103\/RevModPhys.87.925","article-title":"Epidemic processes in complex networks","volume":"87","author":"Castellano","year":"2015","journal-title":"Rev. Mod. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1145\/1232722.1232727","article-title":"The dynamics of viral marketing","volume":"1","author":"Leskovec","year":"2007","journal-title":"ACM Trans. Web."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"025103","DOI":"10.1103\/PhysRevE.69.025103","article-title":"Structural vulnerability of the North American power grid","volume":"69","author":"Albert","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1121\/1.1906679","article-title":"Communication patterns in task-oriented groups","volume":"22","author":"Bavelas","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0378-8733(78)90021-7","article-title":"Centrality in social networks: Conceptual clarification","volume":"1","author":"Freeman","year":"1979","journal-title":"Soc. Netw."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"16569","DOI":"10.1073\/pnas.0507655102","article-title":"An index to quantify an individual\u2019s scientific research output","volume":"102","author":"Hirsch","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"040601","DOI":"10.1103\/PhysRevLett.96.040601","article-title":"K-core organization of complex networks","volume":"96","author":"Dorogovtsev","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1038\/35019019","article-title":"Error and attack tolerance of complex networks","volume":"406","author":"Albert","year":"2000","journal-title":"Nature"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3200","DOI":"10.1103\/PhysRevLett.86.3200","article-title":"Epidemic spreading in scale-free networks","volume":"86","author":"Vespignani","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3682","DOI":"10.1103\/PhysRevLett.86.3682","article-title":"Breakdown of the Internet under intentional attack","volume":"86","author":"Cohen","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1038\/nphys1746","article-title":"Identification of influential spreaders in complex networks","volume":"6","author":"Kitsak","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5547","DOI":"10.1038\/srep05547","article-title":"Searching for super spreaders of information in real-world social media","volume":"4","author":"Pei","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1038\/srep00371","article-title":"Competing activation mechanisms in epidemics on networks","volume":"2","author":"Castellano","year":"2012","journal-title":"Sci. Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9602","DOI":"10.1038\/srep09602","article-title":"Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition","volume":"5","author":"Liu","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"140101","DOI":"10.7498\/aps.62.140101","article-title":"A new approach to identify influential spreaders in complex networks","volume":"62","author":"Hu","year":"2013","journal-title":"Acta Phys. Sin."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0378-8733(83)90028-X","article-title":"Network structure and minimum degree","volume":"5","author":"Seidman","year":"1983","journal-title":"Soc. Netw."},{"key":"ref_24","unstructured":"Batagelj, V., and Zaversnik, M. (arXiv, 2003). An O(m) algorithm for cores decomposition of networks, arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s00778-016-0423-8","article-title":"Incremental k-core decomposition: Algorithms and evaluation","volume":"25","author":"Gedik","year":"2016","journal-title":"VLDB J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2416","DOI":"10.1109\/TPDS.2018.2835441","article-title":"Core Maintenance in Dynamic Graphs: A Parallel Approach Based on Matching","volume":"29","author":"Jin","year":"2018","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/TKDE.2018.2833070","article-title":"I\/O Efficient Core Graph Decomposition: Application to Degeneracy Ordering","volume":"31","author":"Wen","year":"2019","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10168","DOI":"10.1038\/ncomms10168","article-title":"The h-index of a network node and its relation to degree and coreness","volume":"7","author":"Zhou","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.physa.2017.04.088","article-title":"Fast asynchronous updating algorithms for k-shell indices","volume":"482","author":"Lee","year":"2017","journal-title":"Phys. A"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:42:42Z","timestamp":1760186562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,3]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["sym11040477"],"URL":"https:\/\/doi.org\/10.3390\/sym11040477","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,4,3]]}}}