Quantifying influential nodes in complex networks using optimization and particle dynamics: a comparative study

Abstract

In this study, we propose a novel methodology called Particle Dynamics Method (PDM) for identifying and quantifying influential nodes in complex networks. Inspired by Newton’s three laws of motion and the universal gravitation law, PDM is based on a mathematical programming method that leverages node degrees and shortest path lengths. Unlike traditional centrality measures, PDM is easily adaptable to different network sizes and models, making it a versatile tool for network analysis. Our updated version of PDM also considers the direction of each force, resulting in more reliable results. To evaluate PDM’s performance, we tested it on a set of benchmark networks with distinct characteristics and models. Our results demonstrate that PDM outperforms other methodologies in the literature, as removing the identified influential nodes results in a significant decrease in network efficiency and robustness. The key feature of PDM is its flexibility in defining distance, which can be adapted to various network types. For instance, in a transportation network, distance can be defined by the flow between nodes, while in an academic publication system, the quartile of the journal could be used. Our research not only demonstrates the effectiveness of PDM but also highlights the influence of universities in the higher education and global university ranking networks, shedding light on the dynamics of these networks. Our interdisciplinary work has significant potential for collaborations between optimization, physics, and network science. This study opens up avenues for future research, including the extension of PDM to multilayer networks and the generalization of the metrics of monolayer networks for this purpose.