Eur. Phys. J. B 83, 519-524 (2011)
https://doi.org/10.1140/epjb/e2011-20346-0

Regular Article

Topological phase transition in a network model with preferential attachment and node removal

¹ Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK
² Computer Science Department and Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA
³ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
⁴ Rhône Alpes Complex Systems Institute, École Normale Supérieure de Lyon, Université de Lyon 1, 15 parvis René Descartes, BP 7000 69342 Lyon Cedex 07, France

^a e-mail: jrouquie@gmail.com

Received: 5 May 2011
Received in final form: 4 September 2011
Published online: 17 October 2011

Abstract

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.