  We study the problem of testing the existence of a dense subhypergraph. The
null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative
hypothesis is a uniform random hypergraph that contains a dense subhypergraph.
We establish sharp detection boundaries in both scenarios: (1) the edge
probabilities are known; (2) the edge probabilities are unknown. In both
scenarios, sharp detectable boundaries are characterized by the appropriate
model parameters. Asymptotically powerful tests are provided when the model
parameters fall in the detectable regions. Our results indicate that the
detectable regions for general hypergraph models are dramatically different
from their graph counterparts.
