# A multi-core periphery perspective: Ranking via relative centrality

arXiv: https://arxiv.org/abs/2406.04487 · HTML: https://mlsanity.com/paper/2406.04487/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [Optimality of Spectral Clustering in the Gaussian Mixture Model](https://mlsanity.com/paper/1911.00538/) (2019)
- [Clustering and Community Detection in Directed Networks: A Survey](https://mlsanity.com/paper/1308.0971/) (2013)
- [Identification of core-periphery structure in networks](https://mlsanity.com/paper/1409.4813/) (2014)
- [Centrality Measures in Networks](https://mlsanity.com/paper/1608.05845/) (2016)
- [Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths](https://mlsanity.com/paper/1410.6572/) (2014)
- [Multi-scale structure and topological anomaly detection via a new network statistic: The onion decomposition](https://mlsanity.com/paper/1510.08542/) (2015)
- [Finding multiple core-periphery pairs in networks](https://mlsanity.com/paper/1702.06903/) (2017)
- [Core-Periphery Structure in Directed Networks](https://mlsanity.com/paper/1912.00984/) (2019)
- [Core-periphery structure in networks: a statistical exposition](https://mlsanity.com/paper/2202.04455/) (2022)

## Abstract (arXiv)

Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler & Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this coexistence is not well understood and has been pointed out as an open problem (Yanchenko & Sengupta [Statistics Surveys, 2023]). Especially, the impact of inferring the core-periphery structure of a graph on understanding its community structure is not well utilized. In this direction, we introduce a novel quantification for graphs with ground truth communities, where each community has a densely connected part (the core), and the rest is more sparse (the periphery), with inter-community edges more frequent between the peripheries. Built on this structure, we propose a new algorithmic concept that we call relative centrality to detect the cores. We observe that core-detection algorithms based on popular centrality measures such as PageRank and degree centrality can show some bias in their outcome by selecting very few vertices from some cores. We show that relative centrality solves this bias issue and provide theoretical and simulation support, as well as experiments on real-world graphs. Core detection is known to have important applications with respect to core-periphery structures. In our model, we show a new application: relative-centrality-based algorithms can select a subset of the vertices such that it contains sufficient vertices from all communities, and points in this subset are better separable into their respective communities. We apply the methods to 11 biological datasets, with our methods resulting in a more balanced selection of vertices from all communities such that clustering algorithms have better performance on this set.