How directed is a directed network?

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.