  We compare and contrast the stellar structures of isolated Local Group dwarf
galaxies, as traced by their oldest stellar populations, with the satellite
dwarf galaxies of the Milky Way and M31. All Local Group dwarfs with Mv < -6
and surface brightness < 26.5 mags. per square arcsec. are considered, taking
advantage of measurements from surveys that use similar observations and
analysis techniques. For the isolated dwarfs, we use the results from Solitary
Local (Solo) Dwarf Galaxy Survey. We begin by confirming that the structural
and dynamical properties of the two satellite populations are not obviously
statistically different from each other, but we note that there many more
satellites around M31 than around the Milky Way down to equivalent magnitude
and surface brightness limits. We find that dwarfs in close proximity to a
massive galaxy generally show more scatter in their Kormendy relations than
those in isolation. Specifically, isolated Local Group dwarf galaxies show a
tighter trend of half-light radius versus magnitude than the satellite
populations, and similar effects are also seen for related parameters. There
appears to be a transition in the structural and dynamical properties of the
dwarf galaxy population around ~400 kpc from the Milky Way and M31, such that
the smallest, faintest, most circular dwarf galaxies are found closer than this
separation. We discuss the impact of selection effects on our analysis, and we
argue that our results point to the significance of tidal interactions on the
population of systems within approximately 400 kpc from the MW and M31.
