In the recent years, with the increase of using Internet and other new telecommunication technologies, cryptography has become a key area to research and improve in order to transfer data securely between two or more entities, especially when the data transferred classified as a critical or important data. Even there are many encryption algorithms exist, the need of new non-standard encryption algorithms raise to prevent any traditional opportunity to sniff data. The proposed algorithm represents a new encryption algorithm to encrypt and decrypt data securely with the benefits of graph theory properties, the new symmetric encryption algorithm use the concepts of cycle graph, complete graph and minimum spanning tree to generate a complex cipher text using a shared key.