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The Role of Network Size for the Robustness of Centrality Measures

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Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 881))

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Abstract

Measurement errors are omnipresent in network data. Studies have shown that these errors have a severe impact on the robustness of centrality measures. It has been observed that the robustness mainly depends on the network structure, the centrality measure, and the type of error. Previous findings regarding the influence of network size on robustness are, however, inconclusive.

Based on twenty-four empirical networks, we investigate the relationship between global network measures, especially network size and average degree, and the robustness of the degree, eigenvector centrality, and PageRank. We demonstrate that, in the vast majority of cases, networks with a higher average degree are more robust.

For random graphs, we observe that the robustness of Erdős-Rényi (ER) networks decreases with an increasing average degree, whereas with Barabàsi-Albert networks, the opposite effect occurs: with an increasing average degree, the robustness also increases.

As a first step into an analytical discussion, we prove that for ER networks of different size but with the same average degree, the robustness of the degree centrality remains stable.

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Notes

  1. 1.

    We use NetworkX (version 2.2, [12]) to generate random graphs and calculate centrality measures.

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Authors and Affiliations

  1. Institute of Information Systems, Leuphana University of Lüneburg, 21335, Lüneburg, Germany

    Christoph Martin & Peter Niemeyer

Authors
  1. Christoph Martin
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  2. Peter Niemeyer
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Corresponding author

Correspondence to Christoph Martin .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

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Martin, C., Niemeyer, P. (2020). The Role of Network Size for the Robustness of Centrality Measures. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_4

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