Illustration of the classification of galaxies into different LSE categories within the LC-TNGX. The filament spines (yellow dashed lines) are extracted using the DisPerSe algorithm. The clusters, representing the nodes of the cosmic web, are defined as halos with masses of M_200 m > 10^13.5  M_⊙. The dots represent central galaxies in different LSE, such as cluster outskirts (orange), filaments (green), filament-void transition region (red), and voids and walls (purple).