{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T08:32:05Z","timestamp":1777624325970,"version":"3.51.4"},"reference-count":34,"publisher":"Proceedings of the National Academy of Sciences","issue":"21","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2000,10,10]]},"abstract":"<jats:p>\n            We study the statistical properties of a variety of diverse\n real-world networks. We present evidence of the occurrence of three\n classes of small-world networks: (\n            <jats:italic>a<\/jats:italic>\n            ) scale-free\n networks, characterized by a vertex connectivity distribution that\n decays as a power law; (\n            <jats:italic>b<\/jats:italic>\n            ) broad-scale networks,\n characterized by a connectivity distribution that has a power law\n regime followed by a sharp cutoff; and (\n            <jats:italic>c<\/jats:italic>\n            ) single-scale\n networks, characterized by a connectivity distribution with a fast\n decaying tail. Moreover, we note for the classes of broad-scale and\n single-scale networks that there are constraints limiting the addition\n of new links. Our results suggest that the nature of such constraints\n may be the controlling factor for the emergence of different classes of\n networks.\n          <\/jats:p>","DOI":"10.1073\/pnas.200327197","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T14:32:33Z","timestamp":1027693953000},"page":"11149-11152","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":2295,"title":["Classes of small-world networks"],"prefix":"10.1073","volume":"97","author":[{"given":"L. A. N.","family":"Amaral","sequence":"first","affiliation":[{"name":"Center for Polymer Studies and Department of Physics, Boston\r University, Boston, MA 02215"}]},{"given":"A.","family":"Scala","sequence":"additional","affiliation":[{"name":"Center for Polymer Studies and Department of Physics, Boston\r University, Boston, MA 02215"}]},{"given":"M.","family":"Barth\u00e9l\u00e9my","sequence":"additional","affiliation":[{"name":"Center for Polymer Studies and Department of Physics, Boston\r University, Boston, MA 02215"}]},{"given":"H. E.","family":"Stanley","sequence":"additional","affiliation":[{"name":"Center for Polymer Studies and Department of Physics, Boston\r University, Boston, MA 02215"}]}],"member":"341","published-online":{"date-parts":[[2000,9,26]]},"reference":[{"key":"e_1_3_2_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/30918"},{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1515\/9780691188331"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.3180"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/43601"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.286.5439.509"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.2758"},{"key":"e_1_3_2_7_2","unstructured":"Newman M. E. J. (2000) J. Stat. Phys. in\n press."},{"key":"e_1_3_2_8_2","volume-title":"The Small World","author":"Kochen M","year":"1989","unstructured":", ed M Kochen (Ablex, Norwood, NJ The Small World, 1989)."},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/16483"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1038\/350669a0"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1038\/355073a0"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1038\/27427"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511815478"},{"key":"e_1_3_2_14_2","first-page":"161","volume-title":"Behavioral Dimensions of Retirement Economics","author":"Axtell R","year":"1999","unstructured":"R Axtell Behavioral Dimensions of Retirement Economics, ed H J Aaron (Brookings Instit., Washington, DC), pp. 161\u2013183 (1999)."},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1038\/347626a0"},{"key":"e_1_3_2_16_2","first-page":"443","volume":"1696","author":"Adamic L A","year":"1999","unstructured":"L A Adamic The Small World Web Res Adv Tech Digit Libr Proc 1696, 443\u2013452 (1999).","journal-title":"The Small World Web Res Adv Tech Digit Libr Proc"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.280.5360.95"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/43604"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.287.5461.2115a"},{"key":"e_1_3_2_20_2","volume-title":"Handbook of Theoretical Computer Science. Volume A: Algorithms and Complexity","author":"van Leeuwen J","year":"1999","unstructured":", ed J van Leeuwen (Elsevier, Amsterdam Handbook of Theoretical Computer Science. Volume A: Algorithms and Complexity, 1999)."},{"key":"e_1_3_2_21_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B","year":"1985","unstructured":"B Bollob\u00e1s Random Graphs (Academic, London, 1985)."},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4571(199210)43:9<628::AID-ASI5>3.0.CO;2-0"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s100510050359"},{"key":"e_1_3_2_24_2","volume-title":"ACI Annual Worldwide Airports Traffic Reports","year":"1999","unstructured":"ACI Annual Worldwide Airports Traffic Reports (Airport Counc. Int., Geneva, 1999)."},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.2307\/3773626"},{"key":"e_1_3_2_26_2","volume-title":"A Study of a Biased Friendship Net","author":"Fararo T J","year":"1964","unstructured":"T J Fararo, M H Sunshine A Study of a Biased Friendship Net (Syracuse Univ. Press, Syracuse, NY, 1964)."},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1986.0056"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.284.5411.96"},{"key":"e_1_3_2_29_2","volume-title":"Small-World Networks and the Conformation Space of a Lattice Polymer Chain","author":"Scala A","year":"1999","unstructured":"A Scala, L A N Amaral, M Barth\u00e9l\u00e9my Small-World Networks and the Conformation Space of a Lattice Polymer Chain (cond-mat\/0004380, 1999)."},{"key":"e_1_3_2_30_2","first-page":"275","volume-title":"Sociometry and the Science of Man","author":"Bonney M E","year":"1956","unstructured":"M E Bonney Sociometry and the Science of Man, ed J L Moreno (Beacon House, New York), pp. 275\u2013286 (1956)."},{"key":"e_1_3_2_31_2","volume-title":"Sociometry and the Science of Man","author":"Moreno J L","year":"1956","unstructured":"J L Moreno Sociometry and the Science of Man (Beacon House, New York, 1956)."},{"key":"e_1_3_2_32_2","first-page":"607","volume":"48","author":"Simon H A","year":"1958","unstructured":"H A Simon, C P Bonini Am Econ Rev 48, 607\u2013617 (1958).","journal-title":"Am Econ Rev"},{"key":"e_1_3_2_33_2","volume-title":"Skew Distributions and the Sizes of Business Firms","author":"Ijiri Y","year":"1977","unstructured":"Y Ijiri, H A Simon Skew Distributions and the Sizes of Business Firms (North\u2013Holland, Amsterdam, 1977)."},{"key":"e_1_3_2_34_2","volume-title":"Introduction to Phase Transitions and Critical Phenomena","author":"Stanley H E","year":"1971","unstructured":"H E Stanley Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971)."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.200327197","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T11:12:18Z","timestamp":1649848338000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/full\/10.1073\/pnas.200327197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9,26]]},"references-count":34,"journal-issue":{"issue":"21","published-print":{"date-parts":[[2000,10,10]]}},"alternative-id":["10.1073\/pnas.200327197"],"URL":"https:\/\/doi.org\/10.1073\/pnas.200327197","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9,26]]},"assertion":[{"value":"2000-04-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2000-07-13","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2000-09-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}