  When a network is inferred from data, two types of errors can occur: false
positive and false negative conclusions about the presence of links. We focus
on the influence of local network characteristics on the probability $\alpha$ -
of type I false positive conclusions, and on the probability $\beta$ - of type
II false negative conclusions, in the case of networks of coupled oscillators.
We demonstrate that false conclusion probabilities are influenced by local
connectivity measures such as the shortest path length and the detour degree,
which can also be estimated from the inferred network when the true underlying
network is not known a priory. These measures can then be used for
quantification of the confidence level of link conclusions, and for improving
the network reconstruction via advanced concepts of link thresholding.
