# Identification of core-periphery structure in networks

arXiv: https://arxiv.org/abs/1409.4813 · HTML: https://mlsanity.com/paper/1409.4813/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2014.

## Built on by (most cited first, 11 of 11)

- [GraphPFN: A Prior-Data Fitted Graph Foundation Model](https://mlsanity.com/paper/2509.21489/) (2025)
- [Residual2Vec: Debiasing graph embedding with random graphs](https://mlsanity.com/paper/2110.07654/) (2021)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths](https://mlsanity.com/paper/2112.00183/) (2021)
- [Core-periphery Models for Hypergraphs](https://mlsanity.com/paper/2206.00783/) (2022)
- [Learning Sparse Graphs with a Core-periphery Structure](https://mlsanity.com/paper/2110.04022/) (2021)
- [Cluster Attention for Graph Machine Learning](https://mlsanity.com/paper/2604.07492/) (2026)
- [Core-Intermediate-Peripheral Index: Factor Analysis of Neighborhood and Shortest Paths-based Centrality Metrics](https://mlsanity.com/paper/2310.06358/) (2023)
- [A multi-core periphery perspective: Ranking via relative centrality](https://mlsanity.com/paper/2406.04487/) (2024)
- [Uncovering the hidden core-periphery structure in hyperbolic networks](https://mlsanity.com/paper/2406.19953/) (2024)
- [Do Vision Transformers Need All-to-All Attention? Global Communication Through Elastic Learned Cores](https://mlsanity.com/paper/2605.12491/) (2026)

## Abstract (arXiv)

Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of core-periphery structure to observed data using a combination of an expectation--maximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the decomposition itself. We find the method to be efficient, scaling easily to networks with a million or more nodes and we test it on a range of networks, including real-world examples as well as computer-generated benchmarks, for which it successfully identifies known core-periphery structure with low error rate. We also demonstrate that the method is immune from the detectability transition observed in the related community detection problem, which prevents the detection of community structure when that structure is too weak. There is no such transition for core-periphery structure, which is detectable, albeit with some statistical error, no matter how weak it is.