In large computer network design, it is desirable to have connections which achieve the most efficient and reliable communication. In such design, there are several factors which should be considered. Two of the factors which seem to appear most frequently are,(a) the number of connection which can be attached to a computer is limited, and (b) a short communication route between any two computers is required. Thus, it will end up with a large network subject to these constraints. The computer network can be modelled as a graph, where each computer is represented by a vertex, and the connection between the two computers is represented by an edge. In this paper, we compare the efficiency and reliability of computer networks based on their graph topology model. The method used in this study is literature study, designing the new topology, and making simulation and testing using a software simulator called Graphical Network Simulator 3 (GNS3). The results of this study are the comparison of the application of prism and petersen graph topologies in computer networks topology.