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@ARTICLE{Kaiser:888183,
      author       = {Kaiser, Franz and Ronellenfitsch, Henrik and Witthaut,
                      Dirk},
      title        = {{D}iscontinuous transition to loop formation in optimal
                      supply networks},
      journal      = {Nature Communications},
      volume       = {11},
      number       = {1},
      issn         = {2041-1723},
      address      = {[London]},
      publisher    = {Nature Publishing Group UK},
      reportid     = {FZJ-2020-04745},
      pages        = {5796},
      year         = {2020},
      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.},
      cin          = {IEK-STE},
      ddc          = {500},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {153 - Assessment of Energy Systems – Addressing Issues of
                      Energy Efficiency and Energy Security (POF3-153) / ES2050 -
                      Energie Sytem 2050 (ES2050) / VH-NG-1025 - Helmholtz Young
                      Investigators Group "Efficiency, Emergence and Economics of
                      future supply networks" $(VH-NG-1025_20112014)$ / CoNDyNet 2
                      - Kollektive Nichtlineare Dynamik Komplexer Stromnetze
                      (BMBF-03EK3055B)},
      pid          = {G:(DE-HGF)POF3-153 / G:(DE-HGF)ES2050 /
                      $G:(HGF)VH-NG-1025_20112014$ / G:(DE-JUEL1)BMBF-03EK3055B},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:33199688},
      UT           = {WOS:000594725700002},
      doi          = {10.1038/s41467-020-19567-2},
      url          = {https://juser.fz-juelich.de/record/888183},
}