Interconnection networks are critical to high-performance computing systems, where reliability is a key metric for evaluating network efficiency. Connectivity and diagnosability, as two fundamental indicators, play a crucial role in characterizing network reliability. As extensions of classical metrics, \((r+1)\) -component connectivity and \((r+1)\) -component diagnosability provide a more refined assessment of system resilience and fault tolerance. In this paper, we establish the \((r+1)\) -component connectivity of the n-dimensional hierarchical cubic network \(HCN_n\) as \(c\kappa _{r+1}(HCN_n)=-\frac{1}{2}r^2+(n+\frac{1}{2})r+1\) for \(n\ge 3\) and \(1\le r\le n-2\) , where n represents the dimension of \(HCN_n\) , and r denotes the number of components after node removals. Additionally, we determine the \((r+1)\) -component diagnosability of \(HCN_n\) under the Preparata-Metze-Chien model (PMC model) and the generalized Maeng-Malek model (MM* model) as \(ct_{r+1}(HCN_n)=-\frac{1}{2}r^2+(n-\frac{1}{2})r+n+1\) for \(n\ge 3\) and \(1\le r\le n-2\) . Extensive simulations demonstrate that component connectivity consistently outperforms classical, conditional, and structural connectivity metrics, while component diagnosability significantly surpasses their corresponding diagnosability measures in \(HCN_n\) . Although our analysis focuses on the specific regular network \(HCN_n\) , the findings offer valuable insights and underscore the effectiveness of component-based connectivity and diagnosability for a broader class of cube-like networks.
