Optimal path management is an important activity for any network system. The efficiency of a large-scale network depends upon finding the shortest path between any pair of nodes as it helps to minimize the routing cost. The traditional methods like Dijkstra’s and A* algorithms though are good at finding shortest path, but they tend to get slow on very large graphs and suffer from memory problems to store precomputed distances. In this paper, we try to explore Reinforcement learning and neural networks to compute the shortest path. Q-learning, a type of reinforcement learning self learns from environment by considering the topology of nodes and uses the distance between nodes to find the shortest path. The neural network though finds the approximate of an optimal distance but once a neural network is trained, the time taken to compute the shortest distance becomes constant. The paper competes the performance of Q-learning and neural networks in calculating the shortest distance between network nodes and find that neural networks performs better than Q-learning irrespective of the number of nodes used in shortest path computation. The performance of two techniques is compared based on computation time needed to find the shortest path.