A Method Inspired by One-Dimensional Discrete-Time Quantum Walks for Influential Node Identification

Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, this study proposes a novel method inspired by the one-dimensional discrete-time quantum walk (IOQW). This design enables the development of a simplified shift operator that leverages both self-loops and the network's structural connectivity. Furthermore, degree centrality and path-based features are integrated into the coin operator, enhancing the accuracy and scalability of the IOQW framework. Comparative evaluations against state-of-the-art quantum and classical methods demonstrate that IOQW excels in capturing both local and global topological properties while maintaining a low computational complexity of O(N⟨k⟩), where ⟨k⟩ denotes the average degree. These advancements establish IOQW as a powerful and practical tool for influential node identification in complex networks, bridging quantum-inspired techniques with real-world network science applications.