{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T15:28:36Z","timestamp":1778686116978,"version":"3.51.4"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["70971140"],"award-info":[{"award-number":["70971140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdoctoral Research Funding","award":["70971140"],"award-info":[{"award-number":["70971140"]}]},{"name":"Fundamental Research Funds of the Central South University","award":["70971140"],"award-info":[{"award-number":["70971140"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We investigate a class of generalized weighted scale-free networks, where the new vertex connects to<jats:italic>m<\/jats:italic>pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.<\/jats:p>","DOI":"10.1155\/2013\/902519","type":"journal-article","created":{"date-parts":[[2013,3,28]],"date-time":"2013-03-28T17:04:06Z","timestamp":1364490246000},"page":"1-6","source":"Crossref","is-referenced-by-count":2,"title":["Exact Solutions of a Generalized Weighted Scale Free Network"],"prefix":"10.1155","volume":"2013","author":[{"given":"Li","family":"Tan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China"},{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dingyou","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"6684","key":"1","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","volume":"393","year":"1998","journal-title":"Nature"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1126\/science.286.5439.509"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1038\/43601"},{"key":"4","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0378-4371(99)00291-5","volume":"272","year":"1999","journal-title":"Physica A"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.85.4629"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.85.4633"},{"issue":"6 i","key":"7","volume":"63","year":"2001","journal-title":"Physical Review E"},{"key":"8","doi-asserted-by":"crossref","first-page":"5835","DOI":"10.1103\/PhysRevLett.86.5835","volume":"86","year":"2001","journal-title":"Physical Review Letters"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.228701"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.11.011"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.1009"},{"key":"12","year":"1886"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902519.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902519.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902519.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T06:16:13Z","timestamp":1498025773000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/902519\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":12,"alternative-id":["902519","902519"],"URL":"https:\/\/doi.org\/10.1155\/2013\/902519","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}