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

Abstract

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 $\tau = 1$.