In this paper, we propose a new symmetric stream cipher encryption algorithm based on Graph Walks and 2-dimensional matrices, called Matrix Encryption Walks (MEW). We offer example Key Matrices and show the efficiency of the proposed method, which operates in linear complexity with an extremely large key space and low-resource requirements. We also provide the Proof of Concept code for the encryption algorithm and a detailed analysis of the security of our proposed MEW. The MEW algorithm is designed for low-resource environments such as IoT or smart devices and is therefore intended to be simple in operation. The encryption, decryption, and key generation time, along with the bytes required to store the key, are all discussed, and similar proposed algorithms are examined and compared. We further discuss the avalanche effect, key space, frequency analysis, Shannon entropy, and chosen/known plaintext-ciphertext attacks, and how MEW remains robust against these attacks. We have also discussed the potential for future research into algorithms such as MEW, which make use of alternative structures and graphic methods for improving encryption models.