  Core-periphery structure is a common property of complex networks, which is a
composition of tightly connected groups of core vertices and sparsely connected
periphery vertices. This structure frequently emerges in traffic systems,
biology, and social networks via underlying spatial positioning of the
vertices. While core-periphery structure is ubiquitous, there have been limited
attempts at modeling network data with this structure. Here, we develop a
generative, random network model with core-periphery structure that jointly
accounts for topological and spatial information by "core scores" of vertices.
Our model achieves substantially higher likelihood than existing generative
models of core-periphery structure, and we demonstrate how the core scores can
be used in downstream data mining tasks, such as predicting airline traffic and
classifying fungal networks. We also develop nearly linear time algorithms for
learning model parameters and network sampling by using a method akin to the
fast multipole method, a technique traditional to computational physics, which
allow us to scale to networks with millions of vertices with minor tradeoffs in
accuracy.
