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How directed is a directed network?

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We present new methods for calculating trophic levels and coherence in any directed network, improving upon ecological definitions. This approach reveals node functions and network properties across diverse systems.

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Area of Science:

  • Network Science
  • Systems Biology
  • Ecology

Background:

  • Trophic levels and coherence in directed networks offer insights into functional properties and network stability.
  • Existing ecological definitions of trophic levels have limitations, restricting their application to networks with specific structures (e.g., basal nodes).

Purpose of the Study:

  • To propose novel, broadly applicable definitions for trophic levels and coherence in directed networks.
  • To demonstrate the utility of these new definitions in identifying node functions across various network types.
  • To explore the relationship between these network properties and other topological characteristics.

Main Methods:

  • Development of generalized definitions for node trophic levels and network trophic coherence.
  • Application of the proposed method to diverse directed networks, including ecological, supply chain, gene expression, and language networks.
  • Analysis of the correlation between trophic levels/coherence and other network topological features, such as non-normality and cycle structure.

Main Results:

  • The proposed method successfully computes trophic levels and coherence for any directed network, overcoming limitations of previous approaches.
  • Node functions were effectively identified in diverse network examples using the new definitions.
  • The study revealed the degree of global directional alignment within network edges.

Conclusions:

  • The generalized definitions of trophic levels and coherence provide a versatile tool for analyzing directed networks.
  • This framework enhances understanding of network structure, function, and stability across scientific domains.
  • The method offers a new perspective on the directional organization of complex systems.