Probabilistic Prediction in Scale-Free Networks: Diameter Changes

J.-H. Kim, K.-I. Goh, B. Kahng, and D. Kim
Phys. Rev. Lett. 91, 058701 – Published 1 August 2003

Abstract

In complex systems, responses to small perturbations are too diverse to definitely predict how much they would be, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of a single vertex for various in silico and real-world scale-free networks. We find that the diameter changes are indeed diverse and their distribution exhibits an algebraic decay with an exponent ζ asymptotically. Interestingly, the exponent ζ is robust as ζ2.2(1) for most scale-free networks and insensitive to the degree exponents γ as long as 2<γ3. However, there is another type with ζ1.7(1) and its examples include the Internet and its related in silico model.

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  • Received 5 December 2002

DOI:https://doi.org/10.1103/PhysRevLett.91.058701

©2003 American Physical Society

Authors & Affiliations

J.-H. Kim, K.-I. Goh, B. Kahng, and D. Kim

  • School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

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Issue

Vol. 91, Iss. 5 — 1 August 2003

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