Identifying vital nodes by Achlioptas process

TL;DR

This paper introduces a novel method using Achlioptas process-based percolation to identify vital nodes in networks, outperforming traditional centrality measures in various network conditions and showing robustness to noise.

Contribution

The paper presents a new percolation-based approach for vital node identification that surpasses existing centrality methods in accuracy and robustness, with broader solution space.

Findings

The new method outperforms traditional centrality measures in identifying vital nodes.

It is more tolerant to noisy and missing data.

The randomness in the process offers a wider range of optimal solutions.

Abstract

The vital nodes are the ones that play an important role in the organization of network structure or the dynamical behaviours of networked systems. Previous studies usually applied the node centralities to quantify the importance of nodes. Realizing that the percolation clusters are dominated by local connections in the subcritical phase and by global connections in the supercritical phase, in this paper we propose a new method to identify the vital nodes via a competitive percolation process that is based on an Achlioptas process. Compared with the existing node centrality indices, the new method performs overall better in identifying the vital nodes that maintain network connectivity and facilitate network synchronization when considering different network structure characteristics, such as link density, degree distribution, assortativity, and clustering. We also find that our method is more tolerant of noisy data and missing data. More importantly, compared with the unique ranking list of nodes given by most centrality methods, the randomness of the percolation process expands the possibility space of the optimal solutions, which is of great significance in practical applications.