  Many real-world networks are theorized to have core-periphery structure
consisting of a densely-connected core and a loosely-connected periphery. While
this phenomenon has been extensively studied in a range of scientific
disciplines, it has not received sufficient attention in the statistics
community. In this expository article, our goal is to raise awareness about
this topic and encourage statisticians to address the many open inference
problems in this area. To this end, we first summarize the current research
landscape by reviewing the metrics and models that have been used for
quantitative studies on core-periphery structure. Next, we formulate and
explore various inferential problems in this context, such as estimation,
hypothesis testing, and Bayesian inference, and discuss related computational
techniques. We also outline the multidisciplinary scientific impact of
core-periphery structure in a number of real-world networks. Throughout the
article, we provide our own interpretation of the literature from a statistical
perspective, with the goal of prioritizing open problems where contribution
from the statistics community will be most effective and important.
