Here λ i are the eigenvalues of the gyration tensor and λ denotes their mean. This value has the bounds 0 ≤ ∆ ≤ 1, such that if the monomers of a bottlebrush are distributed isotropically around its center-of-mass, ∆ vanishes as the shape resembles a sphere. A nonzero value of ∆ indicates an anisotropic distribution of monomers. We plot the average asphericity ∆ as a function of M bb for a number of side chain molecular weights M sc in We observe shape features consistent with the interpretations of [η], R h , and R g . At low values of M bb , there is a decrease in asphericity as the molecule transitions from a two-armed star (with an asphericity typical of a short polymer chain) to a star-like polymer (second snapshot in Figure ). This star-like molecule begins to elongate approximately as M bb increases beyond the M sc , leading to a marked increase in the value of ∆ . Bottlebrushes with the same M bb but shorter side chains have higher aspect ratio, so ∆ increases with M sc in this region. A similar trend in ∆ with M sc can be seen in prior simulation studies as well. The stiffness of this elongated shape causes it to extend beyond the asphericity of a random coil, and then decrease to the random coil limit at large M bb . This latter region is consistent with the observations that the intrinsic viscosity and R h exhibit scaling exponents ν v and ν h slightly larger than the swollen-coil values.