### 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 [Formula presented] asymptotically. Interestingly, the exponent [Formula presented] is robust as [Formula presented] for most scale-free networks and insensitive to the degree exponents [Formula presented] as long as [Formula presented]. However, there is another type with [Formula presented] and its examples include the Internet and its related in silico model.

Original language | English |
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Journal | Physical review letters |

Volume | 91 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2003 Aug 1 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physical review letters*,

*91*(5). https://doi.org/10.1103/PhysRevLett.91.058701