We investigate k-path complexes \(\mathcal {P}_k(G)\) of finite graphs, defined as the pure \((k-1)\) -dimensional simplicial complexes whose facets correspond to paths of length \(k-1\) in G. Our first main result provides a complete characterization of graphs G for which \(\mathcal {P}_k(G)\) is a simplicial forest or a quasi-forest, and we show that these two notions coincide in this setting. From the algebraic perspective, we establish conditions under which \(\mathcal {P}_k(G)\) is Cohen-Macaulay. For connected graphs G and \(k \in \{3,4,5\}\) , we prove that \(\mathcal {P}_k(G)\) is Cohen-Macaulay whenever it is a simplicial forest. In contrast, we present explicit examples demonstrating that for \(k \ge 6\) , \(\mathcal {P}_k(G)\) may fail to be Cohen-Macaulay even when it forms a simplicial tree.
