Identification of important objectives of networked system based on propagation characteristics

In the context of networked systems, identifying key objectives is crucial for optimizing system efficiency and enhancing capabilities. This study addresses the propagation characteristics of system networks with fixed structures and proposes an improved K-shell decomposition method based on second-order degree decomposition. The traditional degree-based decomposition step is replaced with a second-order degree-based decomposition step. Additionally, within the same second-order degree decomposition KS layer, an enhanced network constraint coefficient is introduced to determine whether nodes within the same KS layer have more structural hole connections. This approach aims to provide a more comprehensive and accurate reflection of the importance of nodes within the network.The proposed method effectively evaluates key propagation nodes in different networks through improved K-shell decomposition and network constraint coefficients. The paper systematically proposes an improved K-shell method based on second-order degree decomposition combined with a network constraint coefficient, validating its efficiency and accuracy in identifying critical propagation nodes through contextual analysis, methodological innovation, experiments on real and synthetic datasets, and comparisons of Kendall's coefficient and SIR propagation simulations.