Immunization for complex network based on the effective degree of vertex

TL;DR

This paper introduces an immunization strategy for complex networks that uses the effective degree of vertices, which considers the current network state, leading to more effective immunization compared to traditional degree-based methods.

Contribution

It proposes a novel immunization approach based on effective degrees that adaptively ranks vertices during the process, improving effectiveness over traditional degree-based strategies.

Findings

Effective degree-based strategies outperform degree-based ones in simulations.

The method is effective on both scale-free and real-world networks.

Simulations show increased network robustness after immunization.

Abstract

The basic idea of many effective immunization strategies is first to rank the importance of vertices according to the degrees of vertices and then remove the vertices from highest importance to lowest until the network becomes disconnected. Here we define the effective degrees of vertex, i.e., the number of its connections linking to un-immunized nodes in current network during the immunization procedure, to rank the importance of vertex, and modify these strategies by using the effective degrees of vertices. Simulations on both the scale-free network models with various degree correlations and two real networks have revealed that the immunization strategies based on the effective degrees are often more effective than those based on the degrees in the initial network.