  Complex networks provide a powerful mathematical representation of complex
systems in nature and society. To understand complex networks, it is crucial to
explore their internal structures, also called structural regularities. The
task of network structure exploration is to determine how many groups in a
complex network and how to group the nodes of the network. Most existing
structure exploration methods need to specify either a group number or a
certain type of structure when they are applied to a network. In the real
world, however, not only the group number but also the certain type of
structure that a network has are usually unknown in advance. To automatically
explore structural regularities in complex networks, without any prior
knowledge about the group number or the certain type of structure, we extend a
probabilistic mixture model that can handle networks with any type of structure
but needs to specify a group number using Bayesian nonparametric theory and
propose a novel Bayesian nonparametric model, called the Bayesian nonparametric
mixture (BNPM) model. Experiments conducted on a large number of networks with
different structures show that the BNPM model is able to automatically explore
structural regularities in networks with a stable and state-of-the-art
performance.
