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.S Online supplementary data available from stacks.iop.org/NJP/16/093001/ mmedia Keywords: community structure, mixture network, probabilistic model, unipartite and bipartite structure 2 New J. Phys. 16 (2014) 093001 C Chang and C Tang drawbacks when used in mixture networks without considering their own characteristics. First, directly using algorithms that can work for bipartite networks, such as biclustering [26] or hierarchical clustering [20], will omit the association between pairs of nodes that are actually one. Such nodes may be partitioned into different modules improperly, even when a community detection algorithm does not allow for an overlapping community or when they are assigned to the same module with two different weights or probabilities. In addition, projecting a mixture network into a unipartite network is an alternative choice [21], but information will be lost in such a process, as it would be for a bipartite network [8,27], and only one vertex set, rather than both, can be assigned to modules following the transformation. Furthermore, imputation methods can be used to convert the second type of mixture networks to unipartite networks by predicting missing values [28]. However, the performance of a community detection algorithm will then depend on the performance of the...
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