Abstract: To address the limitations of existing temporal network models in identifying critical nodes, which often suffer from narrow evaluation perspectives and low computational efficiency, an improved gravity model was proposed for key node recognition. This model integrated both the mixed degree decomposition and degree information of nodes while accounting for their positional influence, effectively capturing both local and global structural characteristics to quantify node importance. The computational complexity was reduced by defining the distance between nodes using a truncated network radius. Experiments were conducted on six real-world datasets using the SIR propagation model, Kendall's correlation coefficient, and Top-k metrics. Results demonstrated that the proposed model outperformed six other methods in identifying critical nodes in temporal networks.

Key words: time series networks, key nodes, gravity model, mix degree decomposition