  In various application areas, networked data is collected by measuring
interactions involving some specific set of core nodes. This results in a
network dataset containing the core nodes along with a potentially much larger
set of fringe nodes that all have at least one interaction with a core node. In
many settings, this type of data arises for structures that are richer than
graphs, because they involve the interactions of larger sets; for example, the
core nodes might be a set of individuals under surveillance, where we observe
the attendees of meetings involving at least one of the core individuals. We
model such scenarios using hypergraphs, and we study the problem of core
recovery: if we observe the hypergraph but not the labels of core and fringe
nodes, can we recover the "planted" set of core nodes in the hypergraph?
  We provide a theoretical framework for analyzing the recovery of such a set
of core nodes and use our theory to develop a practical and scalable algorithm
for core recovery. The crux of our analysis and algorithm is that the core
nodes are a hitting set of the hypergraph, meaning that every hyperedge has at
least one node in the set of core nodes. We demonstrate the efficacy of our
algorithm on a number of real-world datasets, outperforming competitive
baselines derived from network centrality and core-periphery measures.
