In this work, we propose an encryption and decryption algorithm in a computer network, using ideas from graph theory and matrices. We attempt to simulate a method in which data can be transferred efficiently post-encryption. Random complete graphs consisting of 250 vertices and 31125 edges were created, with randomly chosen start and end nodes to depict the initial source and final destination for data transferred. The algorithm harnesses the idea of a random graph and assigns a multi-dimensional weight to each of the nodes. These weights along with a randomly generated path are used to build an encryption matrix which increases the randomness in the encryption, making it a more robust encryption algorithm. We study that how such an algorithm performs. The aim of this exercise is to understand applications of linear algebra to algorithms which can also be used as a learning tool example in cybersecurity.