  We study the properties of a leave-node-out jackknife procedure for network
data. Under the sparse graphon model, we prove an Efron-Stein-type inequality,
showing that the network jackknife leads to conservative estimates of the
variance (in expectation) for any network functional that is invariant to node
permutation. For a general class of count functionals, we also establish
consistency of the network jackknife. We complement our theoretical analysis
with a range of simulated and real-data examples and show that the network
jackknife offers competitive performance in cases where other resampling
methods are known to be valid. In fact, for several network statistics, we see
that the jackknife provides more accurate inferences compared to related
methods such as subsampling.
