  We study the localization of a cluster of activated vertices in a graph, from
adaptively designed compressive measurements. We propose a hierarchical
partitioning of the graph that groups the activated vertices into few
partitions, so that a top-down sensing procedure can identify these partitions,
and hence the activations, using few measurements. By exploiting the cluster
structure, we are able to provide localization guarantees at weaker signal to
noise ratios than in the unstructured setting. We complement this performance
guarantee with an information theoretic lower bound, providing a necessary
signal-to-noise ratio for any algorithm to successfully localize the cluster.
We verify our analysis with some simulations, demonstrating the practicality of
our algorithm.
