Software Defined Network (SDN) is a new networking concept in which the data plane is decoupled from the control plane. Due to the huge demand on network resources and the rapidly increasing numbers of devices needing to be connected to the network, SDN paradigm has emerged as a potential solution for managing and solving such issues. However, SDN still faces many challenges when it comes to its achievable network performance in terms of delay, packet dropped rate, throughput, and other metrics. This thesis studies the impact of SDN topologies on network performances such as end-to-end latency, control packet overhead, and flow setup failure rate. Understanding the nature of each topology and how it is affecting the SDN performance help us make appropriate network design decisions that can enhance SDN systems. In this thesis, we study the impact of the network topology on SDN performances, by simulating the network performance under three different topology scenarios and evaluating the average end-to-end latency, flow setup failure rates and Open Flow control message overhead that are achievable under each of these three scenarios.