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A generalized simplicial model and its application.

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This study introduces a framework to analyze higher-order network structures and their impact on network functions. Regulating 2-simplices significantly alters network performance, offering new insights into complex systems.

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Area of Science:

  • Complex networks
  • Network science
  • Graph theory

Background:

  • Pairwise networks overlook crucial higher-order structural characteristics.
  • Research evaluating higher-order structures' effects on network functions remains limited.

Purpose of the Study:

  • To propose a framework for quantifying the impact of higher-order structures (e.g., 2-simplices) on complex network functions.
  • To develop a simplicial model for regulating 2-simplices while preserving the degree sequence.

Main Methods:

  • Developed a simplicial model to control the quantity of 2-simplices.
  • Maintained the original network's degree sequence during model construction.
  • Compared network performance using the original network and its simplicial model.

Main Results:

  • The framework effectively quantifies the influence of higher-order structures on network functions.
  • Regulating 2-simplices significantly impacts network performance across various functions.
  • The method indirectly controls higher-order simplices (beyond 2-order).

Conclusions:

  • The proposed framework is a general and effective tool for linking higher-order structures with network functions.
  • This approach deepens the understanding of micro-level structures' correlation with global network functions.
  • The framework serves as a valuable reference for diverse applications in network science.