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

Published online by Cambridge University Press:  20 October 2020

Christoph Martin Open the ORCID record for Christoph Martin [Opens in a new window]  and
Peter Niemeyer
Christoph Martin*
Affiliation:
Institute of Information Systems, Leuphana University of Lüneburg 21335 Lüneburg, Germany (e-mail: niemeyer@uni.leuphana.de)
Peter Niemeyer
Affiliation:
Institute of Information Systems, Leuphana University of Lüneburg 21335 Lüneburg, Germany (e-mail: niemeyer@uni.leuphana.de)
*
*Corresponding author. Email: cmartin@uni.leuphana.de
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Abstract

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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 Erdős–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.

Keywords

centrality measuresmeasurement errormissing datarobustness
Type
Research Article
Information
Network Science , Volume 9 , Special Issue S1: Complex Networks 2019 , October 2021 , pp. S61 - S82
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

Special Issue Editor: Hocine Cherifi

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