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Influence of measurement errors on networks: Estimating the robustness of centrality measures

Published online by Cambridge University Press:  05 August 2019

Christoph Martin  and
Peter Niemeyer
Christoph Martin*
Affiliation:
Institute of Information Systems, Leuphana University of Lüneburg, Universitätsallee 1, 21335 Lüneburg, Germany
Peter Niemeyer
Affiliation:
Institute of Information Systems, Leuphana University of Lüneburg, Universitätsallee 1, 21335 Lüneburg, Germany
*
*Corresponding author. Emails: cmartin@uni.leuphana.de, niemeyer@uni.leuphana.de
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Abstract

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Most network studies rely on a measured network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics, especially on centrality measures: a more central node in the observed network might be less central in the underlying network. Previous studies have dealt either with the general effects of measurement errors on centrality measures or with the treatment of erroneous network data. In this paper, we propose a method for estimating the impact of measurement errors on the reliability of a centrality measure, given the measured network and assumptions about the type and intensity of the measurement error. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can, therefore, be used as a basis for decision-making. In our experiments, we apply this method to random graphs and real-world networks. We observe that our estimation is, in the vast majority of cases, a good approximation for the robustness of centrality measures. Beyond this, we propose a heuristic to decide whether the estimation procedure should be used. We analyze, for certain networks, why the eigenvector centrality is less robust than, among others, the pagerank. Finally, we give recommendations on how our findings can be applied to future network studies.

Keywords

centrality measuresmeasurement errormissing datarobustness
Type
Original Article
Information
Network Science , Volume 7 , Issue 2 , June 2019 , pp. 180 - 195
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
© Cambridge University Press 2019

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