Data communication is inevitable in current world of networking and transformation of data securely through the channels is a challenging task due to various threats. This paper presents an efficient cryptographic algorithm for the messages sent across the channels. A graph theoretic approach is implemented for the encryption and decryption process. Messages are converted into graphs and adjacency matrix of the graphs are used for encryption and decryption process. The key which has to be transmitted along with the encrypted message is also encrypted using modular inverse. Then the encrypted message is again converted to a matrix for decryption to get the original message. © 2020, Research Publication. All rights reserved.