多核心-边缘视角：基于相对中心性的排序
A multi-core periphery perspective: Ranking via relative centrality
AI总结：
本文针对图中社区与核心-边缘结构共存问题，提出相对中心性概念以消除传统中心性度量在核心检测中的偏差，并证明基于该方法的顶点子集选择能更均衡地覆盖所有社区，从而提升聚类性能。
摘要：
社区结构和核心-边缘结构是两种被广泛研究的图结构，且二者在真实世界图中被观察到共存（Rombach, Porter, Fowler & Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]）。然而，这种共存的性质尚未被充分理解，并已被指出为一个开放问题（Yanchenko & Sengupta [Statistics Surveys, 2023]）。尤其是，推断图的核心-边缘结构对理解其社区结构的影响尚未得到充分利用。在这一方向上，我们针对具有真实社区标签的图引入了一种新的量化方式，其中每个社区都有一个连接密集的部分（核心），其余部分更稀疏（边缘），并且社区间的边在边缘之间更频繁出现。基于这一结构，我们提出了一种新的算法概念，称之为相对中心性，用于检测核心。我们观察到，基于流行中心性度量（如 PageRank 和度中心性）的核心检测算法在其结果中可能表现出一定偏差，即从某些核心中仅选择极少数顶点。我们证明相对中心性解决了这一偏差问题，并提供了理论和模拟支持，以及在真实世界图上的实验。核心检测已知在核心-边缘结构方面具有重要应用。在我们的模型中，我们展示了一种新的应用：基于相对中心性的算法可以选择一个顶点子集，使得该子集包含来自所有社区的足够多的顶点，并且该子集中的点能够更好地分离到它们各自的社区中。我们将这些方法应用于 11 个生物数据集，我们的方法从所有社区中更均衡地选择顶点，使得聚类算法在该集合上具有更好的性能。
英文摘要：
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.
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