A label-switching algorithm for fast core-periphery identification

TL;DR

This paper introduces a fast, greedy label-switching algorithm for identifying core-periphery structures in networks, improving speed and accuracy over existing methods and demonstrating significant performance gains on synthetic and real-world networks.

Contribution

The paper presents a novel, efficient heuristic algorithm for core-periphery detection that outperforms existing methods in speed and accuracy, with theoretical and empirical validation.

Findings

Algorithm is an order-of-magnitude faster than naive implementations.

Achieves solutions within 90% of the global optimum on toy networks.

On real-world data, it is 340 times faster than competing methods.

Abstract

Core-periphery (CP) structure is frequently observed in networks where the nodes form two distinct groups: a small, densely interconnected core and a sparse periphery. Borgatti and Everett (2000) proposed one of the most popular methods to identify and quantify CP structure by comparing the observed network with an ``ideal'' CP structure. While this metric has been widely used, an improved algorithm is still needed. In this work, we detail a greedy, label-switching algorithm to identify CP structure that is both fast and accurate. By leveraging a mathematical reformulation of the CP metric, our proposed heuristic offers an order-of-magnitude improvement on the number of operations compared to a naive implementation. We prove that the algorithm monotonically ascends to a local maximum while consistently yielding solutions within 90% of the global optimum on small toy networks. On synthetic networks, our algorithm exhibits superior classification accuracies and run-times compared to a popular competing method, and on one-real world network, it is 340 times faster.