<p>Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is no universally accepted definition or method for identifying weather regimes. Recent work has shown that regimes can be interpreted geometrically as topological structures in atmospheric phase space, allowing their detection without prescribing the number of regimes in advance. In this framework, regimes are identified using a density–radius bifiltration combined with persistent homology, a well-established tool in topological data analysis. A limitation of this approach is its reliance on density estimation, which can over-smooth weakly populated yet dynamically meaningful regions of phase space. This limitation is particularly relevant for datasets with weakly separated or sparsely sampled regimes, such as the southern jet regime in the North Atlantic and the thin zonal loops of the Charney–DeVore system. Here, we introduce a centrality–radius bifiltration that emphasizes local connectivity in phase space and overcomes the limitations of the density-based method, in particular by recovering the southern jet regime and the thin loop structures of the Charney–DeVore system. The resulting regime-related topological structures are robust across a range of analysis scales, suggesting that they reflect the intrinsic organization of atmospheric phase space rather than artifacts of parameter choice. The method provides a practical and reproducible diagnostic tool for identifying weather regimes across datasets. We also integrate our method into an existing analysis framework.</p>