  In many networks, vertices have hidden attributes, or types, that are
correlated with the networks topology. If the topology is known but these
attributes are not, and if learning the attributes is costly, we need a method
for choosing which vertex to query in order to learn as much as possible about
the attributes of the other vertices. We assume the network is generated by a
stochastic block model, but we make no assumptions about its assortativity or
disassortativity. We choose which vertex to query using two methods: 1)
maximizing the mutual information between its attributes and those of the
others (a well-known approach in active learning) and 2) maximizing the average
agreement between two independent samples of the conditional Gibbs
distribution. Experimental results show that both these methods do much better
than simple heuristics. They also consistently identify certain vertices as
important by querying them early on.
