In recent years, the demand for data security has exploded in various areas of daily life and society such as science, academia, Networks, industry, financial services, government, telecommunications, media, law and many more. The protection of data has become a major concern over time. Cryptography is the study of secure communication and the protection of data in various fields. However, the complexity and constant evolution of cryptographic algorithms require continuous research and development. In recent years, Graph Theory has emerged to be a valuable tool in the field of cryptography, providing new insights and techniques to ensure the security of communication in networks. The algorithm proposed in this research work develops a graph-based encryption scheme that protects the shared data from being accessed, altered, or interfered with by unwanted and unauthorized parties. The shared symmetric key ensures confidentiality and high security. Not just alphabets; with this algorithm, data including all 256 characters along with their ASCII values can be transmitted securely.