  In this paper, we study the graph realization problem in the Congested Clique
model of distributed computing under crash faults. We consider {\em
degree-sequence realization}, in which each node $v$ is associated with a
degree value $d(v)$, and the resulting degree sequence is realizable if it is
possible to construct an overlay network with the given degrees.
  Our main result is a $O(f)$-round deterministic algorithm for the
degree-sequence realization problem in a $n$-node Congested Clique, of which
$f$ nodes could be faulty ($f<n$). The algorithm uses $O(n^2)$ messages. We
complement the result with lower bounds to show that the algorithm is tight
w.r.t the number of rounds and the messages simultaneously.
  We also extend our result to the Node Capacitated Clique (NCC) model, where
each node is restricted to sending and receiving at-most $O(\log n)$ messages
per round. In the NCC model, our algorithm solves degree-sequence realization
in $O(nf/\log n)$ rounds and $O(n^2)$ messages.
  For both settings, our algorithms work without the knowledge of $f$, the
number of faults. To the best of our knowledge, these are the first results for
the graph realization problem in the crash-fault distributed network.
