On the impact of network size and average degree on the robustness of centrality measures

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Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and ErdÅ's-Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.

Original languageEnglish
JournalNetwork Science
Issue numberS1
Pages (from-to)S61-S82
Number of pages22
Publication statusPublished - 20.10.2021
EventInternational Conference on Complex Networks and their Applications - 2019: Complex Networks - Calouste Gulbenkian Foundation, Lisbon, Portugal
Duration: 10.12.201912.12.2019
Conference number: 8

Bibliographical note

Special Issue S1: Complex Networks 2019. © The Author(s), 2020. Published by Cambridge University Press