# Vulnerability of Clustering under Node Failure in Complex Networks

## TL;DR

This paper investigates how the failure of individual nodes affects the clustering coefficient in complex networks, proposing algorithms to identify critical nodes and demonstrating their effectiveness through experiments.

## Contribution

It formulates the vulnerability of network clustering to node failures as an NP-complete problem and provides two algorithms to identify critical vertices affecting clustering.

## Key findings

- Proven NP-completeness of the vulnerability problem.
- Algorithms effectively identify critical nodes impacting clustering.
- Experimental results outperform other strategies in real and synthetic networks.

## 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 we 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.