Node Importance Evaluation Method Based on Fractional-Order Topological Propagation and Local Information Entropy

Accurate identification of key nodes in complex networks is vital for optimizing system robustness and controlling information spread. Existing centrality metrics struggle to balance the continuous extraction of global topological features with the fine-grained perception of local structures, while traditional heuristic algorithms also face severe resolution limitations. To address these issues, this paper proposes a node importance evaluation method based on fractional-order topological propagation and local information entropy (FSEC). This method overcomes the limitations of discrete integer-order propagation inherent in traditional graph walks. It constructs a continuous fractional-order topological propagation operator within the spectral graph theory framework. This enables the smooth projection of node degree features into the global topological space, thereby yielding high-order global impact factors. Furthermore, an information theory mechanism is introduced to quantify the probability distribution of a node’s information contribution within its local neighborhood. The local structural information entropy is then calculated to reflect the node’s asymmetric control over micro-level information flow. Deliberate attack simulations were conducted on nine real-world networks and three types of artificial network models. The results show that the proposed FSEC algorithm significantly outperforms baseline algorithms like Autoencoder and Graph Neural Network (AGNN), Degree Centrality, k-shell, PageRank, and Mixed Degree Decomposition (MDD) in degrading the largest connected component (LCC) and global network efficiency (NE). The proposed method also achieves the minimum Area Under the Curve (AUC) values globally. Its monotonicity is slightly lower than that of AGNN but superior to all other baseline algorithms. In addition, SIR simulations further confirm the effectiveness of the FSEC method. This approach successfully resolves the ranking tie problem among nodes in the same topological layer.