ArticleProceedings of the National Academy of Sciences of the United States of America2017
Looplessness in networks is linked to trophic coherence.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed.
- Extreme vulnerability to intruder attacks destabilizes network dynamics.Nature communications · 2026Article
- Optimal dismantling of directed networks.Nature communications · 2026Article
- The frequency response of networks as open systems.Nature communications · 2026Article
- Urbanisation Drives the Decoupling, Simplification, and Homogenization of Aquatic and Terrestrial Food Webs.Ecology letters · 2025Article
- The impact of structured higher-order interactions on ecological network stability.Theoretical ecology · 2025Article
- Influence and influenceability: global directionality in directed complex networks.Royal Society open science · 2023Article
- Strong connectivity in real directed networks.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks.Scientific reports · 2021Article
- How directed is a directed network?Royal Society open science · 2020Article
- Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy.Scientific reports · 2020Article
- Resilience or robustness: identifying topological vulnerabilities in rail networks.Royal Society open science · 2019Article
- Structure and dynamical behavior of non-normal networks.Science advances · 2018Article
- The origin of motif families in food webs.Scientific reports · 2017Article
- Universal attenuators and their interactions with feedback loops in gene regulatory networks.Nucleic acids research · 2017Article
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2 authors.
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Abstract
Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been suggested that this architecture can confer advantages to the system as a whole, such as "qualitative stability," but this observation does not in itself explain how a loopless structure might arise. We show here that the number of feedback loops in a network, as well as the eigenvalues of associated matrices, is determined by a structural property called trophic coherence, a measure of how neatly nodes fall into distinct levels. Our theory correctly classifies a variety of networks-including those derived from genes, metabolites, species, neurons, words, computers, and trading nations-into two distinct regimes of high and low feedback and provides a null model to gauge the significance of related magnitudes. Because trophic coherence suppresses feedback, whereas an absence of feedback alone does not lead to coherence, our work suggests that the reasons for "looplessness" in nature should be sought in coherence-inducing mechanisms.
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