The number $σ_k(G)$ of induced subgraphs with size $k$ of a graph $G$ was introduced recently as the number of $k$-nearly independent vertex subsets of $G$. Results highlighting similarity and difference in the behaviours of $σ_1$ and $σ_0$, have been reported. In this paper, we provide more comparison tools, by studying the ratio $\frac{σ_1(G)}{σ_{0}(G)}$. We establish sharp lower and upper bounds for this ratio over various classes of graphs, including connected graphs, trees, and forests.