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Inconsistencies Among Spectral Robustness Metrics

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Quality, Reliability, Security and Robustness in Heterogeneous Systems (Qshine 2018)

Abstract

Network robustness plays a critical role in the proper functioning of modern society. It is common practice to use spectral metrics, to quantify the robustness of networks. In this paper we compare eight different spectral metrics that quantify network robustness. Four of the metrics are derived from the adjacency matrix, the others follow from the Laplacian spectrum. We found that the metrics can give inconsistent indications, when comparing the robustness of different synthetic networks. Then, we calculate and compare the spectral metrics for a number of real-world networks, where inconsistencies still occur, but to a lesser extent. Finally, we indicate how the concept of the \(R^*\)-value, a weighted sum of robustness metrics, can be used to resolve the found inconsistencies.

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Acknowledgements

This research was supported in part by the Netherlands Organization for Scientific Research (NWO) with project number 439.16.107, the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its National Cybersecurity R & D Programme (Award No. NRF 2014NCR-NCR001-40) and administered by the National Cybersecurity R & D Directorate, by the Spanish Ministry of Science and Innovation project GIROS TEC2015-66412-R and by the Generalitat de Catalunya research support program SGR-1469.

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Correspondence to Xiangrong Wang .

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© 2019 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Wang, X., Feng, L., Kooij, R.E., Marzo, J.L. (2019). Inconsistencies Among Spectral Robustness Metrics. In: Duong, T., Vo, NS., Phan, V. (eds) Quality, Reliability, Security and Robustness in Heterogeneous Systems. Qshine 2018. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-030-14413-5_10

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  • DOI: https://doi.org/10.1007/978-3-030-14413-5_10

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