Optimal shattering of complex networks

Nicole Balashov, Reuven Cohen, Avieli Haber, Michael Krivelevich, Simi Haber*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

Original languageEnglish
Article number99
JournalApplied Network Science
Issue number1
StatePublished - 1 Dec 2019


FundersFunder number
Israel National Directorate
USA-Israel BSF2014361
Israel Science Foundation1261/17
Center for Research in Applied Cryptography and Cyber Security, Bar-Ilan University


    • Random graphs
    • Shattering


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