Recommender systems relying on contextual multi-armed bandits continuously improve relevant item recommendations by taking into account the contextual information. The objective of bandit algorithms is to learn the best arm (e.g., best item to recommend) for each user and thus maximize the cumulative rewards from user engagement with the recommendations. The context that these algorithms typically consider are the user and item attributes. However, in the context of social networks where the action of one user can influence the actions and rewards of other users, neighbors' actions are also a very important context, as they can have not only predictive power but also can impact future rewards through spillover. Moreover, influence susceptibility can vary for different people based on their preferences and the closeness of ties to other users which leads to heterogeneity in the spillover effects. Here, we present a framework that allows contextual multi-armed bandits to account for such heterogeneous spillovers when choosing the best arm for each user. Our experiments on several semi-synthetic and real-world datasets show that our framework leads to significantly higher rewards than existing state-of-the-art solutions that ignore the network information and potential spillover.