Random Spatial Network Models with Core-Periphery Structure

TL;DR

This paper introduces a novel generative model for networks with core-periphery structure that integrates spatial and topological data, outperforming existing models and enabling scalable analysis of large networks.

Contribution

The authors develop a new random network model with core scores, incorporating spatial information, and provide efficient algorithms for parameter learning and network sampling.

Findings

Model achieves higher likelihood than existing core-periphery models.

Core scores effectively predict airline traffic and classify fungal networks.

Algorithms scale to networks with millions of vertices with minimal accuracy loss.

Abstract

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.