Theory-Contraction is NP-Complete

I investigate the problem of contracting a dependency-network with respect to any of its nodes. The resulting contraction must not contain the node in question, but must also be a minimal mutilation of the original network. Identifying successful and minimally mutilating contractions of dependency-networks is non-trivial, especially when non-well-founded networks are to be taken into account. I prove that the contraction problem is NP-complete.¹