{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/evolution-of-reference-networks-with-aging","title":"Evolution of reference networks with aging","arxiv_id":"cond-mat/0001419","date":"2000-01-28","proceeding":null,"authors":["S. N. Dorogovtsev","J. F. F. Mendes"],"abstract":"We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\\'{a}si-Albert's model and (ii) to $\\tau^{-\\alpha}$, where $\\tau$ is the age of the old site. We consider $\\alpha$ of any sign although reasonable values are $0 \\leq \\alpha \\leq \\infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\\alpha < 1$. When $\\alpha$ increases from $-\\infty$ to 0, the exponent $\\gamma$ of the distribution of connectivities ($P(k) \\propto k^{-\\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\\'{a}si-Albert's model. The following increase of $\\alpha$ to 1 makes $\\gamma$ to grow to $\\infty$. For $\\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.","url_abs":"https://arxiv.org/abs/cond-mat/0001419v1","url_pdf":"https://arxiv.org/pdf/cond-mat/0001419v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"evolution-of-reference-networks-with-aging","repo_url":"https://github.com/narnolddd/FETA3","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}