The design and analysis of robust network topologies are crucial for enhancing the performance and reliability of distributed systems, such as those found in IoT and wireless sensor networks. Despite extensive research, challenges remain in balancing robustness to delays and noise with the need for low communication overhead. In this paper, we introduce a q-triangular r-regular network model for consensus algorithms, where nodes may experience delays and uncertainties. We derive explicit expressions for the Laplacian eigenvalues of this network and analytically evaluate key performance metrics, including convergence time, network coherence, maximum communication delay, diameter, spectral radius, average clustering coefficient, and average path length, to quantify robustness and delay tolerance. Furthermore, we validate our findings by examining real-world autonomous systems. Our results indicate that the proposed q-triangular network significantly reduces communication delays and enhances resilience to noise, outperforming existing hierarchical network designs. These improvements are attributed to the hierarchical and robust structure of the q-triangulation, which ensures reliable consensus in dynamic environments. The findings suggest that the proposed network model is well-suited for designing scalable and robust distributed systems.