In this paper, we propose a structured hypergraph learning algorithm based on the structure of common statistical dependencies observed in network datasets. By considering the social relations regression model (SRRM) as starting point, we extend the explanatory power of the model by including third-order dependency patterns through a hypergraph which exhibit the multi-clustered behavior of the network data. To unveil the underlying structure of the data, the hypergraph learning problem is considered as a combination of a generalized factor analysis problem, regularized by a smoothness assumption over the network data feature space, and a dictionary learning problem, which can be shown to be solved efficiently. Experimental results in both synthetic and real datasets illustrate the performance of the proposed hypergraph learning method.