# Vulnerability of clustering under node failure in complex networks

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## Abstract

Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or adversarial attacks occurring to elements of the network. In this paper, we study an emerging problem in assessing the robustness of complex networks: the vulnerability of the clustering of the network to the failure of network elements. Specifically, we identify vertices whose failures will critically damage the network by degrading its clustering, evaluated through the average clustering coefficient. This problem is important because any significant change made to the clustering, resulting from element-wise failures, could degrade network performance such as the ability for information to propagate in a social network. We formulate this vulnerability analysis as an optimization problem, prove its NP-completeness and non-monotonicity, and offer two algorithms to identify the vertices most important to clustering. Finally, we conduct comprehensive experiments in synthesized social networks generated by various well-known models as well as traces of real social networks. The empirical results over other competitive strategies show the efficacy of our proposed algorithms.

## Keywords

Network science Local clustering coefficient Network reliability## Notes

### Acknowledgements

The work of Alan Kuhnle and My T. Thai is supported in part by NSF EFRI #1441231 and DTRA HDTRA1-14-1-0055. The work of Nam P. Nguyen is supported in part by the NVIDIA Corporation hardware grant and the The Jess and Mildred Fisher Endowed Professor award, Towson University.

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