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Phys. Rev. E 67, 026123 (2003) [5 pages]

Critical phenomena in networks

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A. V. Goltsev1,2,*, S. N. Dorogovtsev1,2,†, and J. F. F. Mendes1,3,‡
1Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
3Departamento de Física, Universidade do Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal

Received 28 April 2002; published 27 February 2003

We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections P(k). The theory shows that the critical behavior depends in a crucial way on the form of P(k) and differs strongly from the standard mean-field behavior. The critical behavior observed in various networks is analyzed and found to be in agreement with theory.

© 2003 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.67.026123
DOI:
10.1103/PhysRevE.67.026123
PACS:
05.10.-a, 05.40.-a, 05.50.+q, 87.18.Sn

*Email address: goltsev@pop.ioffe.rssi.ru

Email address: sdorogov@fc.up.pt

Email address: jfmendes@fc.up.pt