Digital technology is being used for communication more and more these days. The emergence of broad applications of graph theory and its importance in various sciences opened the way for researchers to adopt it in the field of encryption. Application developers are always searching for new or improved encryption methods, even though there are many different types of algorithms. In this research, a modified cryptography system based on the idea from graph theory was considered. It converts the plaintext into a cycle graph and represents this graph in matrix form. A shared key, K, is used, which increases the complexity of the ciphertext, which is also represented as a graph.