# Karp hardness of a module in a graph

DEFINITION: A set of vertices $$A\subseteq V$$ in a graph $$G(V,E)$$ is called a module if it satisfies the following property:

For every $$v\in V\setminus A$$, either $$A\subseteq N(v)$$ or $$A\cap N(v)=\emptyset$$, where $$N(v)$$ is the neighborhood of $$v$$.

GRAPH-MODULE problem:

Input: An undirected graph $$G(V,E)$$ and a natural number $$k$$

Output: YES if $$G$$ has a module $$A\subseteq V$$ with $$|A|=k$$, otherwise NO

What is the complexity of GRAPH-MODULE problem?