DOI: 10.1209/epl/i2003-00166-9
Europhys. Lett., 61 (4) , pp. 567-572 (2003)

Measuring preferential attachment in evolving networks

H. Jeong^{1, 2}, Z. Néda¹ and A. L. Barabási<sup>1

1</sup>  Department of Physics, University of Notre Dame - Notre Dame, IN 46616, USA
²  Department of Physics, Korea Advanced Institute of Science and Technology Taejon, 305-701, Korea

(Received 2 September 2002; accepted in final form 4 December 2002)

Abstract
A key ingredient of many current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called preferential attachment. Measurements on four networks, namely the science citation network, Internet, actor collaboration and science coauthorship network indicate that the rate at which nodes acquire links depends on the node's degree, offering direct quantitative support for the presence of preferential attachment. We find that for the first two systems the attachment rate depends linearly on the node degree, while for the last two the dependence follows a sublinear power law.

PACS
89.65.-s - Social systems.
89.75.-k - Complex systems.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.

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