Empirical networks often exhibit different meso-scale structures, such as community and core-periphery structure. Core-periphery typically consists of a well-connected core, and a periphery that is well-connected to the core but sparsely connected internally. Most core-periphery studies focus on undirected networks. In this talk we discuss a generalisation of core-periphery to directed networks which yields a family of core-periphery blockmodel formulations in which, contrary to many existing approaches, core and periphery sets are edge-direction dependent. Then we shall focus on a particular structure consisting of two core sets and two periphery sets, and we introduce two measures to assess the statistical significance and quality of this structure in empirical data, where one often has no ground truth. The idea will be illustrated on three empirical networks -- faculty hiring, a world trade data-set, and political blogs.
This is based on joint work with Andrew Elliott, Angus Chiu, Marya Bazzi and Mihai Cucuringu, available at https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0783