Identification of the influential nodes in complex networks based on thenonlinear dynamics of solitons

A soliton is a wave packet that maintains its particle-like and wave-like properties due to the balance betweendispersion and nonlinearity during propagation. By abstracting its main characteristics and allowing it totraverse a complex network according to certain rules, we investigated the relationship between the numberof solitons, the number of walk steps, and the frequency of node appearances in different networks. Usingthe Pearson coefficient, we demonstrated a strong correlation between increasing the number of solitonsand reducing the number of walk steps, as well as decreasing the number of solitons and increasing thenumber of walk steps. We also used the Jaccard coefficient to measure the overlap of important nodes acrossdifferent segments. Finally, we selected four real-world networks, Using an infection model, we obtained therelationship curves of infection rate versus time steps, under the condition that important nodes identifiedby various strategies are used as seed nodes. This provides a unique perspective for recognizing influentialnodes and demonstrates that the important nodes derived from soliton walks are effective in the propagationof information within dynamic infection models.