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Young stellar clusters are believed to inherit the spatial distribution likehierarchical structures of their natal molecular cloud during their formation.However, the change of the structures between the cloud and the young clustersis not well constrained observationally. We select the W40 - Serpens Southregion (~ 7 $\times$ 9 pc$^{2}$) of the Aquila Rift as a testbed andinvestigate hierarchical properties of spatial distribution of young stellarobjects (YSOs) in this region. We develop a minimum spanning tree (MST)-basedmethod to group stars into several levels by successively cutting down edgeslonger than an algorithmically determined critical value. A total of 832 YSOsare divided into 5 levels with 23 groups. For describing the hierarchicalproperties in a controlled way, we construct a set of synthetic sourcedistributions at various fractal dimensions, and apply the same method toexplore their group characters. By comparing the $Q$ parameter and the surfacedensity profiles of the observed and the synthetic data, we find that the YSOobservation matches spatial patterns from multi-fractal dimensions. In theperiphery region where the molecular clouds are more diffuse, the YSO structureis close to a fractal dimension of 2.0, while in the core regions the fractaldimensions are close to 1.6 and 1.4 for the W40 and the Serpens South regions,respectively. Therefore, the YSOs may inherit the fractal pattern of the densepart of the molecular clouds, but such pattern dissipates slowly in severalMyr.

Hierarchical Structure of YSO Clusters in the W40 and Serpens South Region: Group Extraction and Comparison with Fractal Clusters