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A Dynamic Mechanism for Prevalence of Triangles in Competitive Networks
M N Mooij1,2, M Baudena3,4,5, A S von der Heydt6,7
1Mathematical Institute, Utrecht University, Utrecht, The Netherlands. m.n.mooij@uu.nl.
Bulletin of Mathematical Biology
|August 14, 2026
Summary
Triangles in networks may naturally emerge from the need for dynamic stability in ecological systems. This suggests that network clustering could be a signature of stabilizing competition, not just explicit connection rules.
Area of Science:
- Ecology
- Network Science
- Mathematical Biology
Background:
- Triangles are common in real-world networks but not in standard null models.
- Existing explanations involve explicit triadic closure or geometry-based rules.
Purpose of the Study:
- To test the hypothesis that triangles arise from dynamic stability requirements in Lotka-Volterra systems.
- To identify structural properties of interaction graphs influencing stability.
Main Methods:
- Proved coexistence conditions based on coupling strength and maximum graph degree.
- Algorithmically optimized networks with fixed degree sequences.
- Analyzed real-world grassland plant networks.
Main Results:
- Coexistence is guaranteed below 1/max_degree and impossible above 1 coupling strength.
- Higher clustering coefficients correlate with stronger interaction strengths in optimized networks.
- Real-world plant networks show higher clustering than expected by degree sequence alone.
Conclusions:
- Triangles and clustering may naturally emerge as signatures of stabilizing competition in ecological networks.
- Dynamic stability requirements can explain triangle abundance without explicit closure mechanisms.
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