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Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy.

Feng Hu1,2, Kuo Tian1,2, Zi-Ke Zhang3,4

  • 1School of Computer, Qinghai Normal University, Xining 810008, China.

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Summary
This summary is machine-generated.

This study introduces novel hypergraph vital node identification methods (HVC and semi-SAVC) using von Neumann entropy. These methods effectively identify crucial nodes in complex systems by leveraging high-order information, outperforming existing techniques.

Keywords:
high-order line graphhypergraphsaturation effectvital nodesvon Neumann entropy

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Information Theory

Background:

  • Hypergraphs naturally model high-order coupling in complex systems.
  • Identifying vital nodes in hypergraphs using high-order information remains challenging.
  • Existing methods often fail to fully exploit complex network structures.

Purpose of the Study:

  • To propose novel methods for vital node identification in hypergraphs.
  • To integrate high-order network information using von Neumann entropy.
  • To evaluate the effectiveness of these methods in identifying influential and robust nodes.

Main Methods:

  • Developed a von Neumann entropy-based hypergraph vital node identification method (HVC).
  • Introduced an optimized version (semi-SAVC) using quadratic approximation for efficiency.
  • Utilized the high-order line graph structure of hypergraphs to quantify node importance.
  • Compared HVC and semi-SAVC against baseline centrality measures.

Main Results:

  • HVC and semi-SAVC demonstrated superior performance in identifying vital nodes.
  • The methods effectively promote maximum influence and maintain network connectivity.
  • Discovered a 'saturation effect' where higher-order information can hinder identification.

Conclusions:

  • The proposed HVC and semi-SAVC methods are effective for vital node identification in hypergraphs.
  • High-order information integration using von Neumann entropy enhances node importance quantification.
  • The saturation effect highlights the importance of balancing information order for optimal results.