# Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths

arXiv: https://arxiv.org/abs/1410.6572 · HTML: https://mlsanity.com/paper/1410.6572/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2014.

## Built on by (most cited first, 5 of 5)

- [Core-Periphery Principle Guided Redesign of Self-Attention in Transformers](https://mlsanity.com/paper/2303.15569/) (2023)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Graph Spectral Embedding using the Geodesic Betweeness Centrality](https://mlsanity.com/paper/2205.03544/) (2022)
- [A multi-core periphery perspective: Ranking via relative centrality](https://mlsanity.com/paper/2406.04487/) (2024)

## Abstract (arXiv)

We introduce several novel and computationally efficient methods for detecting "core--periphery structure" in networks. Core--periphery structure is a type of mesoscale structure that includes densely-connected core vertices and sparsely-connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that a vertex is a core vertex. Our second method is based on a low-rank approximation of a network's adjacency matrix, which can often be expressed as a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically-generated networks and a variety of networks constructed from real-world data sets.