Signature-based botnet detection methods identify botnets by recognizing Command and Control (C\&C) traffic and can be ineffective for botnets that use new and sophisticate mechanisms for such communications. To address these limitations, we propose a novel botnet detection method that analyzes the social relationships among nodes. The method consists of two stages: (i) anomaly detection in an "interaction" graph among nodes using large deviations results on the degree distribution, and (ii) community detection in a social "correlation" graph whose edges connect nodes with highly correlated communications. The latter stage uses a refined modularity measure and formulates the problem as a non-convex optimization problem for which appropriate relaxation strategies are developed. We apply our method to real-world botnet traffic and compare its performance with other community detection methods. The results show that our approach works effectively and the refined modularity measure improves the detection accuracy.