Scaling of optimal-path-lengths distribution in complex networks.

@article{Kalisky2005ScalingOO,
  title={Scaling of optimal-path-lengths distribution in complex networks.},
  author={Tomer Kalisky and Lidia A. Braunstein and Sergey V. Buldyrev and Shlomo Havlin and Harry Eugene Stanley},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2005},
  volume={72 2 Pt 2},
  pages={
          025102
        }
}
We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the… CONTINUE READING

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