Description: Discontinuous transition to loop formation in optimal supply networks

This title appears in the Scientific Report : 2020

Discontinuous transition to loop formation in optimal supply networks

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...

Personal Name(s):	Kaiser, Franz
	Ronellenfitsch, Henrik / Witthaut, Dirk (Corresponding author)
Contributing Institute:	Systemforschung und Technologische Entwicklung; IEK-STE
Published in:	Nature Communications, 11 (2020) 1, S. 5796
Imprint:	[London] Nature Publishing Group UK 2020
DOI:	10.1038/s41467-020-19567-2
PubMed ID:	33199688
Document Type:	Journal Article
Research Program:	Kollektive Nichtlineare Dynamik Komplexer Stromnetze Helmholtz Young Investigators Group "Efficiency, Emergence and Economics of future supply networks" Energie System 2050 Assessment of Energy Systems – Addressing Issues of Energy Efficiency and Energy Security
Link:	Get full text OpenAccess
	Publikationsportal JuSER

Please use the identifier: http://hdl.handle.net/2128/26270 in citations.
Please use the identifier: http://dx.doi.org/10.1038/s41467-020-19567-2 in citations.

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.