  Social network data are relational data recorded among a group of actors,
interacting in different contexts. Often, the same set of actors can be
characterized by multiple social relations, captured by a multidimensional
network. A common situation is that of colleagues working in the same
institution, whose social interactions can be defined on professional and
personal levels. In addition, individuals in a network tend to interact more
frequently with similar others, naturally creating communities. Latent space
models for network data are useful to recover clustering of the actors, as they
allow to represent similarities between them by their positions and relative
distances in an interpretable low dimensional social space. We propose the
infinite latent position cluster model for multidimensional network data, which
enables model-based clustering of actors interacting across multiple social
dimensions. The model is based on a Bayesian nonparametric framework, that
allows to perform automatic inference on the clustering allocations, the number
of clusters, and the latent social space. The method is tested on simulated
data experiments, and it is employed to investigate the presence of communities
in two multidimensional networks recording relationships of different types
among colleagues.
