  Dynamical scalings for the end-to-end distance $R_{ee}$ and the number of
distinct visited nodes $N_v$ of random walks (RWs) on finite scale-free
networks (SFNs) are studied numerically. $\left< R_{ee} \right>$ shows the
dynamical scaling behavior $\left<R_{ee}({\bar \ell},t)\right>=
\bar{\ell}^\alpha (\gamma, N) g(t/\bar{\ell}^z)$, where $\bar{\ell}$ is the
average minimum distance between all possible pairs of nodes in the network,
$N$ is the number of nodes, $\gamma$ is the degree exponent of the SFN and $t$
is the step number of RWs. Especially, $\left<R_{ee}({\bar \ell},t)\right>$ in
the limit $t \to \infty$ satisfies the relation $\left< R_{ee} \right> \sim
\bar{\ell}^\alpha \sim d^\alpha$, where $d$ is the diameter of network with $d
({\bar \ell}) \simeq \ln N$ for $\gamma \ge 3$ or $d ({\bar \ell}) \simeq \ln
\ln N$ for $\gamma < 3$. Based on the scaling relation $\left< R_{ee} \right>$,
we also find that the scaling behavior of the diameter of networks can be
measured very efficiently by using RWs.
