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We demonstrate the utility of dendrograms at representing the essential features of the hierarchical structure of the isosurfaces for molecular line data cubes. The dendrogram of a data cube is an abstraction of the changing topology of the isosurfaces as a function of contour level. The ability to track hierarchical structure over a range of scales makes this analysis philosophically different from local segmentation algorithms like CLUMPFIND. Points in the dendrogram structure correspond to specific volumes in data cubes defined by their bounding isosurfaces. We further refine the technique by measuring the properties associated with each isosurface in the analysis allowing for a multiscale calculation of molecular gas properties. Using COMPLETE 13CO(1-0) data from the L1448 region in Perseus and mock observations of a simulated data cube, we identify regions that have a significant contribution by self-gravity to their energetics on a range of scales. We find evidence for self-gravitation on all spatial scales in L1448 though not in all regions. In the simulated observations, nearly all of the emission is found in objects that would be self-gravitating if gravity were included in the simulation. We reconstruct the size-line width relationship within the data cube using the dendrogram-derived properties and find it follows the standard relation: s_v ~ R^0.58. Finally, we show that constructing the dendrogram of CO J=1-0 emission from the Orion-Monoceros region allows for the identification of giant molecular clouds in a blended molecular line data set using only a physically motivated definition (self-gravitating clouds with masses 5x10^4 Msun.Comment: 15 pages, 16 figures. Accepted to ApJ. Paper will full resolution figures available at http://people.ok.ubc.ca/erosolo/dendrograms.pd

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