{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T16:50:40Z","timestamp":1769359840312,"version":"3.49.0"},"reference-count":27,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T00:00:00Z","timestamp":1552867200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LHT"],"published-print":{"date-parts":[[2019,3,18]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>There are many complex networks like World-Wide Web, internet and social networks have been reported to be scale-free. The major property of scale-free networks is their degree distributions are in power law form. Generally, the degree exponents of scale-free networks fall into the range of (2, 3). The purpose of this paper is to investigate other situations where the degree exponents may lie outside the range.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>In this paper, analysis has been carried out by varying the degree exponents in the range of (0.5, 4.5). In total, 243 scenarios have been generated with varying network size of 1,000, 2,000 and 4,000, and degree exponents in the range of (0.5, 4.5) using interval of 0.05.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>The following five indicators have been investigated: average density, average clustering coefficient, average path length, average diameter and average node degree. These indicators vary with the network size and degree exponent. If certain indicators do not satisfy with the user requirement using degree exponents of (2, 3), one can further increase or decrease the value with tradeoff. Results recommend that for degree exponents in (0.5, 2), 26 possible scale-free networks can be selected whereas for (3, 4.5), 41 possible scale-free networks can be selected, assuming a 100 percent deviation on the network parameters.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>A tolerance analysis is given for the tradeoff and guideline is drawn to help better design of scale-free network for degree exponents in range of (0.5, 2) and (3, 4.5) using network size 1,000, 2,000 and 4,000. The methodology is applicable to any network size.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/lht-07-2017-0146","type":"journal-article","created":{"date-parts":[[2018,9,11]],"date-time":"2018-09-11T03:47:35Z","timestamp":1536637655000},"page":"57-71","source":"Crossref","is-referenced-by-count":10,"title":["Tolerance analysis in scale-free social networks with varying degree exponents"],"prefix":"10.1108","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7992-9901","authenticated-orcid":false,"given":"Kwok Tai","family":"Chui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chien-wen","family":"Shen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2020092419050529400_ref001","doi-asserted-by":"crossref","first-page":"25058","DOI":"10.1038\/srep25058","article-title":"The early history and emergence of molecular functions and modular scale-free network behavior","volume":"6","year":"2016","journal-title":"Scientific Reports"},{"issue":"5439","key":"key2020092419050529400_ref002","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","year":"1999","journal-title":"Science"},{"issue":"1","key":"key2020092419050529400_ref003","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s13278-016-0415-0","article-title":"Resilience of the world wide web: a longitudinal two-mode network analysis","volume":"6","year":"2016","journal-title":"Social Network Analysis and Mining"},{"issue":"1","key":"key2020092419050529400_ref004","first-page":"243","article-title":"On the numerical study of percolation and epidemic critical properties in networks","volume":"89","year":"2016","journal-title":"The European Physical Journal B"},{"key":"key2020092419050529400_ref005","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/S0378-4371(02)01545-5","article-title":"Efficiency of scale-free networks: error and attack tolerance","volume":"320","year":"2003","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"issue":"4","key":"key2020092419050529400_ref006","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s11280-012-0188-y","article-title":"From the internet of things to embedded intelligence","volume":"16","year":"2013","journal-title":"World Wide Web"},{"key":"key2020092419050529400_ref007","first-page":"arXiv1503.08265","article-title":"Statistical network topology for crisis informetrics","volume-title":"arXiv preprint","year":"2015"},{"issue":"6","key":"key2020092419050529400_ref008","article-title":"Scale-free topology optimization for software-defined wireless sensor networks: a cyber-physical system","volume":"13","year":"2017","journal-title":"Journal of Distributed Sensor Networks"},{"key":"key2020092419050529400_ref009","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.fooweb.2015.07.001","article-title":"A primer on the history of food web ecology: fundamental contributions of fourteen researchers","volume":"4","year":"2015","journal-title":"Food Webs"},{"issue":"4","key":"key2020092419050529400_ref010","doi-asserted-by":"crossref","first-page":"431","DOI":"10.3938\/jkps.70.431","article-title":"Scale-free network analysis of big data for patent litigation cases in the United States","volume":"70","year":"2017","journal-title":"Journal of the Korean Physical Society"},{"issue":"1","key":"key2020092419050529400_ref011","first-page":"e006","article-title":"A spatial biosurveillance synthetic data generator in R","volume":"9","year":"2017","journal-title":"Online Journal of Public Health Informatics"},{"issue":"6840","key":"key2020092419050529400_ref012","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1038\/35082140","article-title":"The web of human sexual contacts","volume":"411","year":"2001","journal-title":"Nature"},{"issue":"3","key":"key2020092419050529400_ref013","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1006\/jtbi.2001.2460","article-title":"Small world patterns in food webs","volume":"214","year":"2002","journal-title":"Journal of Theoretical Biology"},{"key":"key2020092419050529400_ref024","unstructured":"Muchnik, L. (2013), \u201cComplexNetworksPackage, download, complex networks package for MatLab\u201d, available at: www.levmuchnik.net\/Content\/Networks\/ComplexNetworksPackage.html#Download (accessed May 26, 2017)."},{"key":"key2020092419050529400_ref014","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ecolmodel.2016.02.009","article-title":"The structure of a marine tropical food web, and its implications for ecosystem-based fisheries management","volume":"328","year":"2016","journal-title":"Ecological Modelling"},{"issue":"1","key":"key2020092419050529400_ref015","doi-asserted-by":"crossref","first-page":"016131","DOI":"10.1103\/PhysRevE.64.016131","article-title":"Scientific collaboration networks. I. network construction and fundamental results","volume":"64","year":"2001","journal-title":"Physical Review E"},{"issue":"3","key":"key2020092419050529400_ref016","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1006\/jmbi.2001.4526","article-title":"Mapping protein family interactions: intramolecular and intermolecular protein family interaction repertoires in the PDB and yeast","volume":"307","year":"2001","journal-title":"Journal of Molecular Biology"},{"issue":"12","key":"key2020092419050529400_ref017","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1109\/JSAC.2016.2621618","article-title":"Toward energy-efficient and robust large-scale WSNs: a scale-free network approach","volume":"34","year":"2016","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"11","key":"key2020092419050529400_ref018","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.3390\/s16111832","article-title":"Estimation of anonymous email network characteristics through statistical disclosure attacks","volume":"16","year":"2016","journal-title":"Sensors"},{"issue":"5","key":"key2020092419050529400_ref300","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.1109\/TNET.2017.2713530","article-title":"ROSE: Robustness strategy for scale-free wireless sensor networks","volume":"25","year":"2017","journal-title":"IEEE\/ACM Transactions on Networking (TON)"},{"issue":"1","key":"key2020092419050529400_ref025","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1207\/s15516709cog2901_3","article-title":"The large-scale structure of semantic networks: statistical analyses and a model of semantic growth","volume":"29","year":"2005","journal-title":"Cognitive Science"},{"issue":"2","key":"key2020092419050529400_ref019","doi-asserted-by":"crossref","first-page":"022302","DOI":"10.1103\/PhysRevE.94.022302","article-title":"Scale-free networks with exponent one","volume":"94","year":"2016","journal-title":"Physical Review E"},{"issue":"7536","key":"key2020092419050529400_ref020","article-title":"Emergence of disassortative mixing from pruning nodes in growing scale-free networks","volume":"4","year":"2014","journal-title":"Scientific Reports"},{"key":"key2020092419050529400_ref021","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.physa.2013.11.026","article-title":"The spread of computer viruses over a reduced scale-free network","volume":"396","year":"2014","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"issue":"6","key":"key2020092419050529400_ref022","article-title":"Giant component sizes in scale-free networks with power-law degrees and cutoffs","volume":"112","year":"2016","journal-title":"Europhysics Letters"},{"key":"key2020092419050529400_ref023","first-page":"1040","article-title":"Non-planar unclustered Peterson graphs as scale-free models of the Internet of Things","year":"2016"},{"issue":"2","key":"key2020092419050529400_ref026","doi-asserted-by":"crossref","first-page":"022307","DOI":"10.1103\/PhysRevE.95.022307","article-title":"Local clustering in scale-free networks with hidden variables","volume":"95","year":"2017","journal-title":"Physical Review E"}],"container-title":["Library Hi Tech"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/LHT-07-2017-0146\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/LHT-07-2017-0146\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T22:14:48Z","timestamp":1753395288000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/lht\/article\/37\/1\/57-71\/269571"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,18]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3,18]]}},"alternative-id":["10.1108\/LHT-07-2017-0146"],"URL":"https:\/\/doi.org\/10.1108\/lht-07-2017-0146","relation":{},"ISSN":["0737-8831"],"issn-type":[{"value":"0737-8831","type":"print"}],"subject":[],"published":{"date-parts":[[2019,3,18]]}}}