Damage and fluctuations induce loops in optimal transport networks.

@article{Katifori2010DamageAF,
  title={Damage and fluctuations induce loops in optimal transport networks.},
  author={Eleni Katifori and Gergely J. Sz{\"o}llősi and Marcelo O. Magnasco},
  journal={Physical review letters},
  year={2010},
  volume={104 4},
  pages={
          048704
        }
}
Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e., loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high… 

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