The rapid growth of the Internet of Things (IoT) has introduced problems of network strength, security, and efficient data management. Classic architectures of IoT are frequently lacking in the mathematical rigor needed to resist dynamic threats and network failures. Although graph-theoretic and algebraic approaches were investigated separately, their joint application is underutilized. This research seeks to fill this gap by combining discrete mathematics and applied algebra to develop strong network architecture for the IoT system. The proposed Discrete Algebraic Network Architecture (DANA) applies graph theory in topology optimization, and algebraic structures for safe data transfer. Algebraic cryptographic protocols, group theory for key management, ring theory for error correction are key parts. Experimental measurements show that DANA enhances network robustness, data reliability, and latency of the network significantly over traditional IoT models. The proposed architecture delivers robustness of 96%, data integrity of 95% and low latency of 18 ms with a high security level of 384 bits.