  Relational inference leverages relationships between entities and links in a
network to infer information about the network from a small sample. This method
is often used when global information about the network is not available or
difficult to obtain. However, how reliable is inference from a small labelled
sample? How should the network be sampled, and what effect does it have on
inference error? How does the structure of the network impact the sampling
strategy? We address these questions by systematically examining how network
sampling strategy and sample size affect accuracy of relational inference in
networks. To this end, we generate a family of synthetic networks where nodes
have a binary attribute and a tunable level of homophily. As expected, we find
that in heterophilic networks, we can obtain good accuracy when only small
samples of the network are initially labelled, regardless of the sampling
strategy. Surprisingly, this is not the case for homophilic networks, and
sampling strategies that work well in heterophilic networks lead to large
inference errors. These findings suggest that the impact of network structure
on relational classification is more complex than previously thought.
