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Scalability is a significant issue in system-on-a-chip architectures because of the rapid increase in numerous on-chip resources. Moreover, hybrid processing elements demand diverse communication requirements, which system-on-a-chip architectures are unable to handle gracefully. Network-on-a-chip architectures have been proposed to address the scalability, contention, reusability, and congestion-related problems of current system-on-a-chip architectures. The reliability appears to be a challenging aspect of network-on-a-chip architectures because of the physical faults introduced in post-manufacturing processes. Therefore, to overcome such failures in network-on-a-chip architectures, fault-tolerant routing is critical. In this article, a network adaptive fault-tolerant routing algorithm is proposed, where the proposed algorithm enhances an efficient dynamic and adaptive routing algorithm. The proposed algorithm avoids livelocks because of its ability to select an alternate outport. It also manages to bypass congested regions of the network and balances the traffic load between outports that have an equal number of hop counts to its destination. Simulation results verified that in a fault-free scenario, the proposed solution outperformed a fault-tolerant XY by achieving a lower latency. At the same time, it attained a higher flit delivery ratio compared to the efficient dynamic and adaptive routing algorithm. Meanwhile, in the situation of a faulty network, the proposed algorithm could reach a higher flit delivery ratio of up to 18% while still consuming less power compared to the efficient dynamic and adaptive routing algorithm.