ArticleNature communications2020
Discontinuous transition to loop formation in optimal supply networks.
Article in Nature communications, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
3 citing papers in PubMed.
- A complex network perspective on brain disease.Biological reviews of the Cambridge Philosophical Society · 2026Review
- Breakthrough-induced loop formation in evolving transport networks.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Dual communities in spatial networks.Nature communications · 2022Article
Corrections and comments
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding redundant edges to supply networks is costly, yet beneficial for resilience. Loops typically form when costs for new edges are small or inputs uncertain. Here, we shed further light on the transition to loop formation. We demonstrate that loops emerge discontinuously when decreasing the costs for new edges for both an edge-damage model and a fluctuating sink model. Mathematically, new loops are shown to form through a saddle-node bifurcation. Our analysis allows to heuristically predict the location and cost where the first loop emerges. Finally, we unveil an intimate relationship among betweenness measures and optimal tree networks. Our results can be used to understand the evolution of loop formation in real-world biological networks.
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Registered trials
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