Graph is hugely used to represent different types of computer and communication networks. One of these networks is the Vehicular Ad Hoc Network (VANET) in which vehicles are represented by vertices and the communication channels are represented by edges. Also, the basic graph algorithms such as breadth first search, depth first search, and shortest path are widely used in VANET graph topology. In such algorithms, the computation time are necessary to be minimized for saving vehicle resources and reduce communication delay particularly in emergency communication. The existing graph representation methods such as adjacency matrix and adjacency list cause VANET algorithms to consume much time. Therefore, we propose a graph representation method based on HashMap of ArrayList that contains pairs of strings and numerical values. The results show that the proposed representation method significantly reduces the computation time of selected graph algorithms particularly when the number of vehicles is large.