Detecting Core-Periphery Structure in Spatial Networks

The core-periphery structure, which decompose a network into a densely-connected core and a sparsely-connected periphery, constantly emerges from spatial networks such as traffic, biological and social networks. In this paper, we propose a random network model for spatial networks with core-periphery structure, which is inspired by the Kleinberg small-world model. In this model, we use a vertex core score to indicate the "coreness" of each vertex, and we connect each pair of vertices with a probability parameterized by their distance and core scores. We compute the optimal vertex core scores in a network by fitting it to our model using a maximum likelihood estimation. Results in real-world networks indicate that the fitted vertex core scores are informative machine learning features for vertex metadata prediction and network classification. Furthermore, we develop near linear-time algorithms for network generation and model inference by using the fast multipole method, which allow us to scale to networks with millions of vertices with minor tradeoffs in accuracy.