  We consider degree-biased random walkers whose probability to move from a
node to one of its neighbors of degree $k$ is proportional to $k^{\alpha}$,
where $\alpha$ is a tuning parameter. We study both numerically and
analytically three types of characteristic times, namely: i) the time the
walker needs to come back to the starting node, ii) the time it takes to visit
a given node for the first time, and iii) the time it takes to visit all the
nodes of the network. We consider a large data set of real-world networks and
we show that the value of $\alpha$ which minimizes the three characteristic
times is different from the value $\alpha_{\rm min}=-1$ analytically found for
uncorrelated networks in the mean-field approximation. In addition to this, we
found that assortative networks have preferentially a value of $\alpha_{\rm
min}$ in the range $[-1,-0.5]$, while disassortative networks have $\alpha_{\rm
min}$ in the range $[-0.5, 0]$. We derive an analytical relation between the
degree correlation exponent $\nu$ and the optimal bias value $\alpha_{\rm
min}$, which works well for real-world assortative networks. When only local
information is available, degree-biased random walks can guarantee smaller
characteristic times than the classical unbiased random walks, by means of an
appropriate tuning of the motion bias.
