The $\underline{\text{path number}}$ of a graph is the minimum number of paths we need to partition the vertices of a graph. Given a connected graph with the independence number $k > 1$, what is the maximum possible value for the path number in this graph? Find the answer in terms of $k$.

The independence number of a graph $\textbf{G}$ is the maximum possible number $k$, such that there exist $k$ pairwise non-adjacent vertices in $\textbf{G}$.