Gaussian Decay Centrality: A quantum-inspired method for identifying important nodes in complex networks

Abstract

In complex networks, critical nodes play a pivotal role in facilitating information propagation. Traditional methods for characterizing node importance often suffer from distortions in capturing dynamic attributes. To address this, inspired by the Gaussian wave packet probability density framework, we developed a novel method to evaluate node importance. This method establishes a Gaussian decay mechanism based on wave packet dynamics, which quantitatively models the exponential decay relationship between node importance and the square of topological distance. Additionally, it incorporates a path weight operator derived from the geometric mean of node degrees to capture the conduction enhancement effect between hub nodes. Furthermore, it introduces an initial influence distribution driven by eigenvector centrality to characterize the intrinsic propagation potential of nodes. Experiments were conducted on 8 real-world networks and 45 synthetic networks. Using the true rankings obtained from the SIR model, we calculated the Kendall’s correlation coefficient $\tau$ between the rankings generated by different methods and the true rankings. The proposed method achieved the best results on multiple networks, and the $\tau$ values of it steadily improved as the infection rate in the SIR model increased. Furthermore, experiments confirmed that the seed nodes selected by our method achieved wider propagation coverage in real-world social networks, highlighting its practical value in real-world information dissemination scenarios. In addition, comprehensive analysis using MI and RDF experiments further validated that the proposed method exhibits optimal monotonicity in its ranking results. Comprehensive analysis using MI and RDF experiments confirmed that the proposed method achieves optimal monotonicity in ranking results.