We investigate the physical relationship between the open clusters Berkeley 6 (Be 6) and S1 using astrometric and photometric data from Gaia Data Release 3 (DR3). Previous studies have suggested that S1 may be a physical companion or substructure associated with Berkeley 6, motivating a detailed kinematic and photometric comparison. We analyze stellar proper motions, parallaxes, and Gaia G, BP, and RP photometry within a spatial region encompassing both clusters.

Probable cluster members are identified using Vector Point Diagrams (VPDs) combined with the HDBSCAN density-based clustering algorithm applied in proper-motion space, allowing probabilistic membership determination while minimizing field-star contamination. High-confidence members are subsequently examined through color–magnitude diagrams (CMDs) constructed from Gaia photometry. The CMDs of both groups reveal a well-defined and nearly identical main sequence, with no statistically significant differences in turn-off features or sequence dispersion.

Further constraints are obtained via manual isochrone fitting using PARSEC stellar evolution models. Although the fit is not exact—owing to observational scatter and residual field contamination—a single isochrone provides a reasonable and consistent representation of the combined stellar population. The derived parameters suggest an age of approximately 200 Myr, sub-solar metallicity (Z ≈ 0.008), and a heliocentric distance of about 2.9 kpc.

The strong agreement in proper-motion distributions, CMD morphology, and broadly consistent physical parameters indicates that Berkeley 6 and S1 are unlikely to be independent clusters, instead representing different regions or substructures of a single, extended open cluster. This study demonstrates that the combined use of Gaia DR3 astrometry and HDBSCAN-based membership selection is an effective approach for investigating the physical association and internal structure of nearby open clusters within the Galactic disk.