We investigate the problem of truth discovery based on opinions from multiple agents (who may be unreliable or biased) that form a social network. We consider the case where agents' reliabilities or biases are correlated if they belong to the same community, which defines a group of agents with similar opinions regarding a particular event. An agent can belong to different communities for different events, and these communities are unknown a priori. We incorporate knowledge of the agents' social network in our truth discovery framework and develop Laplace variational inference methods to estimate agents' reliabilities, communities, and the event states. We also develop a stochastic variational inference method to scale our model to large social networks. Simulations and experiments on real data suggest that when observations are sparse, our proposed methods perform better than several other inference methods, including majority voting, TruthFinder, AccuSim, the Confidence-Aware Truth Discovery method, the Bayesian classifier combination (BCC) method, and the community BCC method.