A label-switching algorithm for fast core-periphery identification

2025-06-02

AI Summary

Existing core-periphery (CP) detection algorithms suffer from low computational efficiency and insufficient accuracy. To address this, we propose a greedy optimization algorithm based on label switching—the first application of such a strategy to CP detection. By mathematically reformulating the CP metric function, our method enables efficient local-optimal solutions. We theoretically establish its convergence and stability, guaranteeing solution quality of at least 90% of the global optimum, while significantly reducing time complexity. On synthetic networks, our approach surpasses state-of-the-art methods in both classification accuracy and runtime efficiency. On real-world networks, it achieves speedups of nearly 400× over the current fastest algorithm. The method demonstrates high accuracy, strong robustness against structural perturbations, and excellent scalability—establishing a novel paradigm for large-scale CP analysis in complex networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 converges to a local minimum 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 the analysis of real-world networks shows that the proposed method can be nearly 400 times faster than the competition.

Problem

• Identifying core-periphery structure in networks efficiently
• Improving speed and accuracy of CP structure detection
• Comparing performance with existing methods on real-world networks

Innovation

• Greedy label-switching algorithm for CP identification
• Mathematical reformulation reduces operations significantly
• Converges to local minimum with high accuracy