In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities. Such multi-relational data can be represented as multi-layer graphs where the set of vertices represents the entities and multiple types of edges represent the different relations among them. For community detection in multi-layer graphs, we consider two random graph models, the multi-layer stochastic blockmodel and a model with a restricted parameter space. We derive consistency results for community assignments of the maximum likelihood estimators in both models. The simulation studies and real data applications confirm the superior performance of the multi-layer approaches in comparison to the baseline procedures.