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

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 $\mathrm{\ell }$ between vertices of the network scales with $n\mathrm{/}{n}^{\ast }$, with $n^{\ast }(p\ll 1)sim{p}^{-\tau }$ and $\tau \approx 2\mathrm{/}3$. We show analytically that $\tau$ cannot be lower than 1 and perform numerical simulations showing that $\tau =1$.