Reducing CLIQUE to Super Connector problem
The simplest NP-hardness reduction is as follows. Suppose we are given an instance $(G,k)$ of CLIQUE. If $k \leq c$ then we solve CLIQUE by brute force in time $O(n^c)$. Otherwise, $G$ has a $k$-clique iff it has a $k$-clique consisting of super-connectors. This is because any vertex in a $k$-clique must have degree at least $k-1 \geq c$, and so is a super-concentrator.