Interference is ubiquitous when conducting causal experiments over social networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). The independent-set design enhances the performance of causal estimators by trading sample quantity for sample quality. We show the capacity of our approach for various causal inference tasks, justify its superiority over conventional methods, and illustrate the empirical performance through simulations.