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Strong connectivity in real directed networks.

Niall Rodgers1,2, Peter Tiňo3, Samuel Johnson1,4

  • 1School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom.

Proceedings of the National Academy of Sciences of the United States of America
|March 17, 2023
PubMed
Summary
This summary is machine-generated.

Strong connectivity in directed networks is not determined by random graph theory but by hierarchical ordering. This trophic coherence property is key to understanding network behavior and resilience.

Keywords:
directed networksfeedbackpercolation theorystrong connectivitytrophic incoherence

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Area of Science:

  • Network science
  • Complex systems
  • Graph theory

Background:

  • Current network theory, based on random graphs, posits that strong connectivity depends on mean degree and degree-degree correlations.
  • However, many real-world directed networks exhibit a very small strongly connected component, contradicting this theory.
  • This discrepancy has significant implications for understanding network properties and system dynamics.

Purpose of the Study:

  • To investigate the factors governing strong connectivity in real-world directed networks.
  • To identify a new metric for network structure that better explains observed connectivity patterns.
  • To analyze the impact of network directionality on connectivity and resilience.

Main Methods:

  • Utilized percolation theory to identify critical points between weakly and strongly connected regimes.
  • Introduced and measured 'trophic coherence' as a metric for hierarchical ordering in networks.
  • Analyzed diverse real-world networks, including ecological, neural, trade, and social networks.

Main Results:

  • Found that strong connectivity critically depends on the network's overall direction or hierarchical ordering, quantified by trophic coherence.
  • Identified the critical point separating weakly and strongly connected network regimes using percolation theory.
  • Confirmed these findings across multiple real-world network types.

Conclusions:

  • Trophic coherence is a crucial factor in determining strong connectivity in directed networks, challenging traditional random graph models.
  • Network connectivity and dynamical processes are highly sensitive to the hierarchical structure.
  • Targeted attacks on edges opposing the network's direction can significantly disrupt connectivity, highlighting the importance of a small fraction of edges.