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.

基于核心 - 边缘结构的新算法概念，相对中心性，能够更好地选择来自所有社区的顶点子集，以提高聚类算法的性能。