Identification of influential vertices in complex networks: A hitting time‐based approach

Abstract

Unravelling the dynamics of network vertices is pivotal, and traditional centrality measures have limitations in adapting to structural changes, directed and weighted networks, and temporal analyses. This paper introduces a ground breaking approach ‐ hitting time‐based centrality. Utilizing network matrix notations and a random walk model on a connected network , we establish a Markov chain to quantify the hitting time, hitting distance, and hitting centrality, providing a nuanced measure prioritizing central vertices. Through extensive experiments using Kendall's tau coefficient, the paper evaluates the method's correlation with actual influence in the Susceptible‐Infectious (SI) model, showcasing superior performance across diverse network sizes and structures. The hitting centrality method exhibits sensitivity to connectivity dynamics, effective incorporation of temporal dynamics, and robust handling of weighted and directed networks. Positive Kendall's tau coefficients underline the method's proficiency in prioritizing influential vertices by correlating hitting centrality values with actual infection ability. The demonstrated robustness to structural changes enhances its utility for dynamic network analysis. In conclusion, our hitting time‐based centrality approach emerges as a promising method, mitigating the shortcomings of traditional measures. By integrating information propagation speed, accommodating network dynamics, and enabling time‐dependent analyses, it offers a comprehensive tool for evaluating vertex importance and influence in complex networks.