Advances in technology and computers are utilized in various fields of contemporary applications, especially in cryptography and data security in graph theory applications. By understanding the concepts of graph theory, researchers and developers can design cryptographic algorithms that are stronger, more efficient and resistant to attacks. One of the cryptographic applications that has been implemented is the XNOR algorithm. This algorithm has been applied to encryption and decryption as well as the use of stream ciphers. By using 64 bits, the XNOR algorithm can expand encryption and decryption capabilities and increase the security of encrypted data. In this research, an analysis was carried out regarding information encryption and decryption algorithms with the application and development of the XNOR gate logic circuit method in Boolean algebra and graph theory. This research uses the example of the word MATH, which can be changed into a code or password and vice versa to secure information that you want to keep secret. Apart from that, an analysis of the graph formation of each character in the word MATH was also carried out using Python which produced semi-Euler and Hamilton graphs