GraphShed: A Data-derived Graph-based waterShed Group Finder

Abstract

This study introduces GraphShed, a data-derived group-finder that applies top-down watershed segmentation to Voronoi-induced graphs, identifying galaxy systems directly from the density field via a GraphShed-derived linking length, with no density thresholds or tunable parameters. A GraphShed galaxy group catalog compared to a Friends-of-Friends (FoF) catalog built from the IllustrisTNG100-1 simulation with a box size of $\sim 75$ Mpc/h yielding $1067$ and $987$ systems, respectively. The GraphShed-derived linking length adapts to the global clustering power of the sample, varying by $\sim 18 \%$ relative to FoF across different sample selections; thus, catalog differences originate in the watershed segmentation. Cross-catalog comparison shows that $\sim 58 \%$ of FoF systems are identically reproduced by GraphShed, $\sim 5 \%$ are completely removed, and the remainder are partially shaved and/or split into multiple systems. While the $M_{200}$ distributions of the two catalogs are statistically consistent, other structural properties including, $R_{200}$, sphericity, compactness, spin, and centroid shift, differ significantly in at least some richness ranges. The unweighted two-point correlation function of GraphShed systems exhibits a higher amplitude on small scales, $r \lesssim 1$ Mpc/h, and agrees with FoF for $r\gtrsim 5$ Mpc/h. A velocity-based classification reveals that GraphShed resolves more interacting pairs than FoF, demonstrating its ability to distinguish nearby overdense structures that position-only methods merge into single systems. These results demonstrate that GraphShed preserves cosmological statistics while providing a more resolved detection of galaxy systems and their dynamical interactions.