Statistical inference for core-periphery structures

TL;DR

This paper develops a statistical framework to quantify, detect, and validate core-periphery structures in networks, providing theoretical guarantees and distinguishing between different types of CP structures.

Contribution

It introduces a model-agnostic parameter for CP strength, establishes label recovery guarantees, and creates tests to differentiate exogenous and endogenous CP structures.

Findings

The framework accurately recovers CP labels in synthetic data.

Statistically significant CP structures are rare in real-world networks.

The tests effectively distinguish between different types of CP structures.

Abstract

Core-periphery (CP) structure is an important meso-scale network property where nodes group into a small, densely interconnected {core} and a sparse {periphery} whose members primarily connect to the core rather than to each other. While this structure has been observed in numerous real-world networks, there has been minimal statistical formalization of it. In this work, we develop a statistical framework for CP structures by introducing a model-agnostic and generalizable population parameter which quantifies the strength of a CP structure at the level of the data-generating mechanism. We study this parameter under four canonical random graph models and establish theoretical guarantees for label recovery, including exact label recovery. Next, we construct intersection tests for validating the presence and strength of a CP structure under multiple null models, and prove theoretical guarantees for type I error and power. These tests provide a formal distinction between exogenous (or induced) and endogenous (or intrinsic) CP structure in heterogeneous networks, enabling a level of structural resolution that goes beyond merely detecting the presence of CP structure. The proposed methods show excellent performance on synthetic data, and our applications demonstrate that statistically significant CP structure is somewhat rare in real-world networks.