ERRATUM: Identifying overlapping communities as well as hubs and outliers via nonnegative matrix factorization

Community detection is important for understanding networks. Previous studies observed that communities are not necessarily disjoint and might overlap. It is also agreed that some outlier vertices participate in no community, and some hubs in a community might take more important roles than others. Each of these facts has been independently addressed in previous work. But there is no algorithm, to our knowledge, that can identify these three structures altogether. To overcome this limitation, we propose a novel model where vertices are measured by their centrality in communities, and define the identification of overlapping communities, hubs, and outliers as an optimization problem, calculated by nonnegative matrix factorization. We test this method on various real networks, and compare it with several competing algorithms. The experimental results not only demonstrate its ability of identifying overlapping communities, hubs, and outliers, but also validate its superior performance in terms of clustering quality.