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Entropy Change in Reversible Processes01:10

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Eigenvalue-based entropy in directed complex networks.

Yan Sun1,2,3, Haixing Zhao1,3, Jing Liang1,3

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

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This study introduces a new method to measure entropy in directed networks, crucial for understanding complex systems. The research quantifies structural information in directed networks, offering insights into network dynamics.

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Area of Science:

  • Network Science
  • Information Theory
  • Graph Theory

Background:

  • Entropy is vital for network analysis, but existing methods primarily focus on undirected networks.
  • Directed networks, with their asymmetric transfers, require specialized entropy measures for accurate structural quantification.
  • Modeling directed complex networks presents significant challenges due to the complexity of node connections.

Purpose of the Study:

  • To propose a directed network model that accounts for the direction of node connections.
  • To define and investigate eigenvalue-based entropies for key matrices in directed networks.
  • To analyze these entropies across various directed complex network models.

Main Methods:

  • Developed a directed network model based on typical complex network structures (nearest-neighbor coupling, small-world, scale-free, random).
  • Defined and calculated eigenvalue entropies for the adjacency matrix, in-degree Laplacian matrix, and in-degree signless Laplacian matrix.
  • Simulated experiments on real-world directed networks for validation.

Main Results:

  • Calculated eigenvalue entropies for directed nearest-neighbor coupling, small-world, scale-free, and random networks.
  • Demonstrated that the eigenvalue entropy of real directed networks falls between that of directed scale-free and small-world networks.
  • Provided a quantitative method for assessing structural information in directed networks.

Conclusions:

  • The proposed directed network model and eigenvalue entropy calculations offer a novel approach to network analysis.
  • The findings highlight the distinct entropy characteristics of different directed network types.
  • This research significantly advances the understanding and quantification of structural properties in complex directed networks.