Social network data often involve transitivity, homophily on observed attributes, clustering, and heterogeneity of actors. We propose the latent cluster random effects model to take account of all of these features, and we describe a Bayesian estimation method. The model fits two real datasets well. We show by simulation that networks with the same degree distribution can have very different clustering behaviors. This suggests that scale-free and small-world network models may not be adequate for all types of network, while our model recovers both the clustering and the degree distribution.