A version of the longest simple cycle problem - NP-completeness reduction proof
In order to prove NP-completeness of a given problem $\Pi$, it is enough to prove that $\Pi \in$ NP and that there exists a polynomial time reduction from any NP-complete problem $\Pi^*$ to $\Pi$.  The reduction must take instances of $\Pi^*$ and return instances of $\Pi$, in polynomial time, such that the answer is the same in both $\Pi^*$ and $\Pi$.  

A suitable reduction from Hamiltonian Circuit has been proposed in a comment to the question: just add enough (that is $n$) isolated vertices to the graph.