Physica A 350 (2005) 622–642 Noisy scale-free networks Jan Scholz a,b , Matha¨us Dejori a,c , Martin Stetter a , Martin Greiner a,Ã a Corporate Technology, Information & Communications, Siemens AG, D-81730 Mu¨nchen, Germany b Institut fu¨r Theoretische Physik, Justus Liebig Universita¨t,Heinrich-Buff-Ring 16, D-35392 GieX en, Germany c Institut fu¨r Informatik, TU Mu¨nchen, BoltzmannstraX e 3,D-85748 Garching, Germany Received 23 August 2004; received in revised form 13 October 2004 Available online 26 November 2004 Abstract The impact of observational noise on the analysis of scale-free networks is studied. Various noise sources are modeled as random link removal, random link exchange and random link addition. Emphasis is on the resulting modifications for the node-degree distribution and for a functional ranking based on betweenness centrality. The implications for estimated gene- expressed networks for childhood acute lymphoblastic leukemia are discussed. r 2004 Elsevier B.V. All rights reserved. PACS: 89.75.k; 89.75.Hc; 87.15.Kg; 05.40.Ca; 02.50.Ey Keywords: Complex networks; Scale-free networks; Gene regulatory networks; Noise 1. Introduction Driven by the science of complex networks [1–3], network biology has become a popular approach to understand the basic structure and dynamics of the complex ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.11.012 Ã Corresponding author. Tel.: +49 89 636 49500; fax: +49 89 636 49767. E-mail addresses: jan.c.scholz@physik.uni-giessen.de (J. Scholz), mathaeus.dejori.external@mchp.siemens.de (M. Dejori), stetter@siemens.com (M. Stetter), martin.greiner@siemens.com (M. Greiner).