Enhanced Key Node Identification in Complex Networks Based on Fractal Dimension and Entropy-Driven Spring Model

Area of Science:

• Network Science
• Complex Systems Analysis
• Computational Graph Theory

Background:

• Identifying critical nodes is crucial for understanding and managing complex networks.
• Traditional centrality methods often rely on limited local or global network information.
• Existing approaches may struggle with multi-scale networks and the "rich-club" phenomenon.

Purpose of the Study:

• To propose a novel model for accurately identifying key nodes in complex networks.
• To overcome limitations of traditional centrality methods by incorporating diverse network properties.
• To enhance the robustness and efficiency of critical node detection.

Main Methods:

• Developed the Second-Order Neighborhood Entropy Fuzzy Local Dimension Spring Model (SNEFLD-SM).
• Integrated second-order neighborhood centrality, betweenness centrality, and fractal dimension within a spring model framework.
• Incorporated information entropy and node influence range, with an attenuation factor to mitigate the "rich-club" effect.

Main Results:

• SNEFLD-SM demonstrated higher accuracy in critical node detection compared to traditional methods across six test networks.
• The model effectively captures network self-similarity and hierarchical structures using fractal technology.
• Information entropy enhanced the model's ability to distinguish node importance and reduced computational costs.

Conclusions:

• SNEFLD-SM offers a more accurate and comprehensive approach to identifying key nodes in complex networks.
• The integration of fractal dimensions and information entropy provides superior analysis of multi-scale network properties.
• The model's ability to suppress the "rich-club" phenomenon improves its applicability to diverse network structures.