Universität zu Köln

Kaiser, Franz ORCID: 0000-0002-7089-2249, Ronellenfitsch, Henrik ORCID: 0000-0002-7799-3368 and Witthaut, Dirk (2020). Discontinuous transition to loop formation in optimal supply networks. Nat. Commun., 11 (1). BERLIN: NATURE RESEARCH. ISSN 2041-1723

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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. Supply networks with optimal structure do not contain loops but these can arise as a result of damages or fluctuations. Here Kaiser et al. uncover the mechanisms of loop formation, predict their location and draw analogies with loop formation in biological networks such as plants and animal vasculature.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kaiser, Franz UNSPECIFIED orcid.org/0000-0002-7089-2249 UNSPECIFIED Ronellenfitsch, Henrik UNSPECIFIED orcid.org/0000-0002-7799-3368 UNSPECIFIED Witthaut, Dirk UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-311312
DOI:	10.1038/s41467-020-19567-2
Journal or Publication Title:	Nat. Commun.
Volume:	11
Number:	1
Date:	2020
Publisher:	NATURE RESEARCH
Place of Publication:	BERLIN
ISSN:	2041-1723
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language LEAF VENATION; BETWEENNESS CENTRALITY; OPTIMIZATION; PERCOLATION; ROBUSTNESS; RESILIENCE; ALGORITHM; EVOLUTION; SYSTEMS; DESIGN Multiple languages Multidisciplinary Sciences Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/31131