  We study the properties of conformal prediction for network data under
various sampling mechanisms that commonly arise in practice but often result in
a non-representative sample of nodes. We interpret these sampling mechanisms as
selection rules applied to a superpopulation and study the validity of
conformal prediction conditional on an appropriate selection event. We show
that the sampled subarray is exchangeable conditional on the selection event if
the selection rule satisfies a permutation invariance property and a joint
exchangeability condition holds for the superpopulation. Our result implies the
finite-sample validity of conformal prediction for certain selection events
related to ego networks and snowball sampling. We also show that when data are
sampled via a random walk on a graph, a variant of weighted conformal
prediction yields asymptotically valid prediction sets for an independently
selected node from the population.
