  We consider navigation or search schemes on networks which are realistic in
the sense that not all search chains can be completed. We show that the
quantity $\mu = \rho/s_d$, where $s_d$ is the average dynamic shortest distance
and $\rho$ the success rate of completion of a search, is a consistent measure
for the quality of a search strategy. Taking the example of realistic searches
on scale-free networks, we find that $\mu$ scales with the system size $N$ as
$N^{-\delta}$, where $\delta $ decreases as the searching strategy is improved.
  This measure is also shown to be sensitive to the distintinguishing
characteristics of networks. In this new approach, a dynamic small world (DSW)
effect is said to exist when $\delta \approx 0$. We show that such a DSW indeed
exists in social networks in which the linking probability is dependent on
social distances.
