An improved gravity centrality based on degree-mixed clustering coefficient and return random walk for identifying influential nodes in complex networks

Identifying influential nodes in complex networks is fundamental for understanding information diffusion, epidemic control, and network resilience. Conventional centrality measures often rely solely on local or global topological features while neglecting dynamic interactions, leading to limited accuracy. To address this issue, we propose an Improved Gravity Centrality based on Degree-Mixed Clustering Coefficient and Return Random Walk (DMCIGC) that integrates both structural and dynamic characteristics. DMCIGC constructs the degree-mixed clustering coefficient hybrid index based on merging node degree and clustering coefficient, and incorporates information entropy into an improved return random walk framework to capture dynamic distances. Experiments on multiple real-world networks datasets demonstrate that DMCIGC effectively detects nodes with dual influence, which are locally central and globally cohesive across the network. Comparative analyses show that DMCIGC consistently outperforms classical centrality measures in spreading ability, achieving the highest average Kendall rank correlation coefficient of 0.6940, which is 0.023 higher than the runner-up across the evaluated datasets. Overall, this study presents a unified and efficient framework for influential node identification, bridging local-global and static-dynamic perspectives in complex network analysis.