2002/12/31 by J. -H. Kim, Jee-Hyub Kim, K. -I. Goh +4
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.91.058701
published as Phys. Rev. Lett. 91, 058701 (2003) · 4 pages, 4 figures, 1 table, final version appeared in PRL
openalex publication_date 2003/08/01 · arxiv created 2003/09/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 zeta asymptotically. Interestingly, the exponent zeta is robust as zeta approximately 2.2(1) for most scale-free networks and insensitive to the degree exponents gamma as long as 2<gamma</=3. However, there is another type with zeta approximately 1.7(1) and its examples include the Internet and its related in silico model.