  We consider the problem of finding an edge in a hidden undirected graph $G =
(V, E)$ with $n$ vertices, in a model where we only allowed queries that ask
whether or not a subset of vertices contains an edge. We study the non-adaptive
model and show that while in the deterministic model the optimal algorithm
requires $\binom{n}{2}$ queries (i.e., querying for any possible edge
separately), in the randomized model $\tilde{\Theta}(n)$ queries are sufficient
(and needed) in order to find an edge.
  In addition, we study the query complexity for specific families of graphs,
including Stars, Cliques, and Matchings, for both the randomized and
deterministic models.
  Lastly, for general graphs, we show a trade-off between the query complexity
and the number of rounds, $r$, made by an adaptive algorithm. We present two
algorithms with $O(rn^{2/r})$ and $\tilde{O}(rn^{1/r})$ sample complexity for
the deterministic and randomized models, respectively.
