We study core-periphery structure in networks using inference methods based
on a flexible network model that allows for traditional onion-like cores within
cores, but also for hierarchical tree-like structures and more general
non-nested types of structure. We propose an efficient Monte Carlo scheme for
fitting the model to observed networks and report results for a selection of
real-world data sets. Among other things, we observe an empirical distinction
between networks showing traditional core-periphery structure with a dense core
weakly connected to a sparse periphery, and an alternative structure in which
the core is strongly connected both within itself and to the periphery.
Networks vary in whether they are better represented by one type of structure
or the other. We also observe structures that are a hybrid between
core-periphery structure and community structure, in which networks have a set
of non-overlapping cores that correspond roughly to communities, surrounded by
a single undifferentiated periphery. Computer code implementing our methods is
available.Comment: code available: https://github.com/apolanco115/hc