This paper examines the propagation of rumors over various social network structures. We create two modified compartmental SIR models by bridging concepts from graph theory, network theory, and epidemic modeling. We incorporate these models in three complex networks: Complete Graph, Small World, and Preferential Attachment. Then, we conduct numerical simulations through modeling software to study the speed, intensity, duration, and extent of the spreading rumor through each structure. Finally, we compare the results between the simulations and pinpoint the underlying characteristics of each network. Our results show that large centralized hubs are more effective in rumor spreading than small, dispersed, but highly connected communities. We also find that by increasing the infection rate or creating more connections within a network both lead to a faster spreading and overall larger final rumor size.