Node influence evaluation method based on saturation propagation probability and multi-level propagation

One of the key areas in network science is assessing node influence in complex networks. Most current methods rely on a constant propagation probability to evaluate node importance, which often fails to capture the dynamic nature of information propagation. To address this limitation, we propose a novel method for node influence evaluation based on saturation propagation probability (SPP) and multi-level propagation characteristics. First, we define the saturation propagation probability (SPP) to model the non-linear dynamics of information propagation, which enables a more accurate evaluation of a node’s propagation influence by dynamically adjusting its propagation ability. Second, we account for both same-order and different-order neighbor interactions in the propagation process, incorporating network topology for a more comprehensive evaluation. Through extensive experiments comparing SPP with seven existing methods across ten networks, we demonstrate its superior performance. Specifically, the SPP method achieves optimal ranking accuracy in all ten networks, delivers the best node similarity performance on 80% of the networks, and consistently performs well in terms of Kendall’s coefficient τ under varying infection rates. These results confirm the method’s effectiveness and applicability in complex networks.