Comment on ``Small-world networks: Evidence for a crossover picture''

Details Comment on ``Small-world networks: Evidence for a crossover picture'' Comment on ``Small-world networks: Evidence for a crossover picture''

1999-03-22

arxiv.org/abs/cond-mat/9903323v1

Physics

Condensed Matter

Statistical Mechanics

2 pages, latex, 2 postscript figures

Scientific paper

In a recent letter (cond-mat/9903108), Barthelemy and Nunes Amaral discuss the crossover phenomenon between regular and ``small-world'' networks, as a function of the network size $n$ and of the disorder $p$. They claim that the average distance $\ell$ between vertices of the network scales with $n / n^*$, with $n^*(p \ll 1) sim p^{-\tau}$ and $\tau \approx 2/3$. We show analytically that $\tau$ cannot be lower than 1 and perform numerical simulations showing that $\tau = 1$.

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