  Finding community structures in networks is important in network science,
technology, and applications. To date, most algorithms that aim to find
community structures only focus either on unipartite or bipartite networks. A
unipartite network consists of one set of nodes and a bipartite network
consists of two nonoverlapping sets of nodes with only links joining the nodes
in different sets. However, a third type of network exists, defined here as the
mixture network. Just like a bipartite network, a mixture network also consists
of two sets of nodes, but some nodes may simultaneously belong to two sets,
which breaks the nonoverlapping restriction of a bipartite network. The mixture
network can be considered as a general case, with unipartite and bipartite
networks viewed as its limiting cases. A mixture network can represent not only
all the unipartite and bipartite networks, but also a wide range of real-world
networks that cannot be properly represented as either unipartite or bipartite
networks in fields such as biology and social science. Based on this
observation, we first propose a probabilistic model that can find modules in
unipartite, bipartite, and mixture networks in a unified framework based on the
link community model for a unipartite undirected network [B Ball et al (2011
Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both
overlapping and nonoverlapping communities) and apply it to two real-world
networks: a southern women bipartite network and a human transcriptional
regulatory mixture network. The results suggest that our model performs well
for all three types of networks, is competitive with other algorithms for
unipartite or bipartite networks, and is applicable to real-world networks.
