Topological Centrality in Gaia Open Clusters
Abstract
Open clusters exhibit diverse spatial structures that provide insight into their formation and dynamical evolution. We investigate the relationship between stellar mass segregation, network topology, and dynamical age in 871 dynamically unevolved open clusters (τ= t/trh ≤ 1) from Gaia-based catalogs. We construct three-dimensional k-nearest-neighbor graphs and measure Degree Centrality (DC), Closeness Centrality (CL), and Betweenness Centrality (BC). For each measure, we define a network-based mass segregation ratio (MSR) by comparing the mean centrality of the most massive stars with that of all cluster members. We test the stability of these measures across connectivity parameters k=5--20 and compare them with the classical 3D MSR, ΛMSR,3D, and dynamical age. All three network ratios show positive correlations with ΛMSR,3D, strongest for closeness centrality, while their correlations with dynamical age are weak. These results demonstrate that network analysis provides a complementary approach to studying stellar structure and mass segregation in open clusters.
Related
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- A Multi-dimensional Analysis of the Open Clusters NGC 2423 and NGC 2482 with Gaia DR3
- The dispersal law of young star clusters: free expansion -- A Gaia/eROSITA census of Orion and Sco--Cen
- High-Priority Compact-Object Candidates in Young Clusters from the \textit{Gaia} DR3 Non-Single-Star Catalog
- A Hierarchical Bayesian Differential Calibration of the Gaia DR3 Parallax Zero Point Using Galactic Globular Clusters
BibTeX
@misc{zaidyn2026topological,
title = {{Topological Centrality in Gaia Open Clusters}},
author = {Marat Zaidyn and Aknur Sakan and Atilkhan Nodyarov and Aigerim Akniyazova and Alisher Zhunuskanov and Nurzhan Ussipov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36897},
eprint = {2610.36897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36897},
}
RIS
TY - UNPB
TI - Topological Centrality in Gaia Open Clusters
AU - Marat Zaidyn
AU - Aknur Sakan
AU - Atilkhan Nodyarov
AU - Aigerim Akniyazova
AU - Alisher Zhunuskanov
AU - Nurzhan Ussipov
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36897
UR - https://arxiv.org/abs/2610.36897
AB - Open clusters exhibit diverse spatial structures that provide insight into their formation and dynamical evolution. We investigate the relationship between stellar mass segregation, network topology, and dynamical age in 871 dynamically unevolved open clusters (τ= t/t_rh ≤ 1) from Gaia-based catalogs. We construct three-dimensional k-nearest-neighbor graphs and measure Degree Centrality (DC), Closeness Centrality (CL), and Betweenness Centrality (BC). For each measure, we define a network-based mass segregation ratio (MSR) by comparing the mean centrality of the most massive stars with that of all cluster members. We test the stability of these measures across connectivity parameters k=5--20 and compare them with the classical 3D MSR, Λ_MSR,3D, and dynamical age. All three network ratios show positive correlations with Λ_MSR,3D, strongest for closeness centrality, while their correlations with dynamical age are weak. These results demonstrate that network analysis provides a complementary approach to studying stellar structure and mass segregation in open clusters.
ER -