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A comparative study of network robustness measures

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Abstract

The robustness is an important functionality of networks because it manifests the ability of networks to resist failures or attacks. Many robustness measures have been proposed from different aspects, which provide us various ways to evaluate the network robustness. However, whether these measures can properly evaluate the network robustness and which aspects of network robustness these measures can evaluate are still open questions. Therefore, in this paper, a thorough introduction over attacks and robustness measures is first given, and then nine widely used robustness measures are comparatively studied. To validate whether a robustness measure can evaluate the network robustness properly, the sensitivity of robustness measures is first studied on both initial and optimized networks. Then, the performance of robustness measures in guiding the optimization process is studied, where both the optimization process and the obtained optimized networks are studied. The experimental results show that, first, the robustness measures are more sensitive to the changes in initial networks than to those in optimized networks; second, an optimized network may not be useful in practical situations because some useful functionalities, such as the shortest path length and communication efficiency, are sacrificed too much to improve the robustness; third, the robustness of networks in terms of closely correlated robustness measures can often be improved together. These results indicate that it is not wise to just apply the optimized networks obtained by optimizing over one certain robustness measure into practical situations. Practical requirements should be considered, and optimizing over two or more Received February 22, 2016; accepted September 29, 2016 E-mail: neouma@163.com suitable robustnessmeasures simultaneously is also a promising way.

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Acknowledgements

This work was partially supported by the Excellent Young Scholars Program of National Natural Science Foundation of China (NSFC) (61522311), the General Program of NSFC (61271301), the Overseas, Hong Kong & Macao Scholars Collaborated Research Program of NSFC (61528205), the Research Fund for the Doctoral Program of Higher Education of China (20130203110010), and the Fundamental Research Funds for the Central Universities (K5051202052).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an, 710071, China

    Jing Liu, Mingxing Zhou, Shuai Wang & Penghui Liu

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  1. Jing Liu
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  2. Mingxing Zhou
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  3. Shuai Wang
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  4. Penghui Liu
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Corresponding author

Correspondence to Jing Liu.

Additional information

Jing Liu is an awardee of the NSFC Excellent Young Scholars Program in 2015. She received the BS degree in computer science and technology and the PhD degree in circuits and systems from Xidian University (XDU), China in 2000 and 2004, respectively. In 2005, she joined XDU as a lecturer, and was promoted to a full professor in 2009. From 2007 to 2008, she was a post-doctoral research fellow with the University of Queensland, Australia, and from 2009 to 2011, she was a research associate with the University of New South Wales - Canberra, Australia. She is currently a full professor with the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, XDU. Her research interests include evolutionary computation, complex networks, fuzzy cognitive maps, multiagent systems, and data mining. She is the associate editor of IEEE Trans. Evolutionary Computation.

Mingxing Zhou received the BS degree in intelligence science and technology from Xidian University (XDU), China and the MS degree in circuits and systems from the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, XDU in 2013 and 2016, respectively. His research interests include evolutionary algorithms, complex networks, and data mining.

Shuai Wang received the BS degree in intelligence science and technology from Xidian University (XDU), China in 2015. Now, he is pursuing the PhD degree in circuits and systems from the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, XDU. His research interests include complex networks and evolutionary algorithms.

Penghui Liu received the BS degree in physics from Xidian University (XDU), China in 2015. Now, he is pursuing the MS degree in circuits and systems from the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, XDU. His research interests include complex networks and evolutionary games.

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Liu, J., Zhou, M., Wang, S. et al. A comparative study of network robustness measures. Front. Comput. Sci. 11, 568–584 (2017). https://doi.org/10.1007/s11704-016-6108-z

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  • DOI: https://doi.org/10.1007/s11704-016-6108-z

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