Social conventions are useful self-sustaining protocols for groups to coordinate behavior without a centralized entity enforcing coordination. The emergence of such conventions in different multi agent network topologies has been investigated by several researches. Although we have performed an exhaustive study of different network structures, we are concerned that different topologies will affect the emergence in different ways. Therefore, the main research question in this work has been comparing and studing effects of different topologies on the emergence of social conventions. While others have investigated memory for learning algorithms, the effects of memory on the reward have not been investigated thoroughly.  We propose a reward metric that is derived directly from the history of the interacting agents. Another research question to be answered is what effect does the history based reward function and the learning approach have on convergence time in different topologies. We also investigate the effects of history size, agent population size and neighborhood size, number of players in the micro interactions and number of actions available proving their effects by agent-based experimentation.