Minimizing the effective graph resistance by adding links is NP-hard

Robert E. Kooij*, Massimo A. Achterberg

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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The effective graph resistance, also known as the Kirchhoff index, is metric that is used to quantify the robustness of a network. We show that the optimisation problem of minimizing the effective graph resistance of a graph by adding a fixed number of links, is NP-hard.

Original languageEnglish
Pages (from-to)601-604
Number of pages4
JournalOperations Research Letters
Issue number6
Publication statusPublished - 2023


  • Effective graph resistance
  • Graph augmentation
  • NP-hard


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