In this work, we integrate `social' interactions into the MARL setup through a user-defined relational network and examine the effects of agent-agent relations on the rise of emergent behaviors. Leveraging insights from sociology and neuroscience, our proposed framework models agent relationships using the notion of Reward-Sharing Relational Networks (RSRN), where network edge weights act as a measure of how much one agent is invested in the success of (or `cares about') another. We construct relational rewards as a function of the RSRN interaction weights to collectively train the multi-agent system via a multi-agent reinforcement learning algorithm. The performance of the system is tested for a 3-agent scenario with different relational network structures (e.g., self-interested, communitarian, and authoritarian networks). Our results indicate that reward-sharing relational networks can significantly influence learned behaviors. We posit that RSRN can act as a framework where different relational networks produce distinct emergent behaviors, often analogous to the intuited sociological understanding of such networks.