Enhancing network robustness through node reinforcement: A voting-based approach

School of Mathematics and Statistics, Shandong University - Weihai 264209, China

Received: 31 January 2026
Accepted: 7 April 2026

Abstract

Developing robust network systems that can sustain functionality after random failures or malicious attacks is a vital problem in complex networks. Many works have focused on improving the robustness of the network. However, these works are based on link manipulation, including swapping links, adding links, and reinforcing links. In this paper, we propose a method that reinforces nodes to improve the robustness of networks. In the proposed method, all nodes vote for their neighbors in each turn, and the voting ability of neighbors of the elected node will decrease in subsequent turns. Experimental results on multiple real-world networks demonstrate that our method significantly outperforms traditional centrality-based protection strategies in enhancing network robustness, achieving an optimal balance between defense effectiveness and resource efficiency.