Small-World Networks: Evidence for a Crossover Picture

  title={Small-World Networks: Evidence for a Crossover Picture},
  author={Marc Barthelemy and Luis A. Nunes Amaral},
  journal={Physical Review Letters},
Watts and Strogatz [Nature (London) 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a ``small world.'' Here, we test the hypothesis that the appearance of small-world behavior is not a phase transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ensuremath{\ell… Expand
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