Strong connectivity in real directed networks

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.