Given a simple graph $G$, A subset of vertices $V_G$ is called very independent if there is no edge between each pair of the vertices in $V_G$ and for each pair $v,v'$, there is no vertex which is connected to both $v$ and $v'$.  In other words, a very independent subset is an independent subset of vertices like $V_G$ such that there is no path of length $2$ or less than it, between each pair of vertices in $V_G$.  How can we prove that the problem of finding a very independent set of size at least $k$ in a given simple graph is NP-Complete?  Note: I was thinking of reducing it to the problem of finding an independent set of size $k$... But, Is that even NP-Complete? 
Problem of finding a very independent set of size at least $k$ is NP-Complete
graphs;np complete