  Determining the mass-radius ($M$-$R$) relation of exoplanets is important for
exoplanet characterization. Here we present a re-analysis of the $M$-$R$
relations and their transitions using exoplanetary data from the PlanetS
catalog which only includes planets with reliable mass and radius
determinations. We find that "small planets" correspond to planets with masses
of up to $\sim4.4 M_\oplus$ (within 17%) where $R \propto M^{0.27}$. Planets
with masses between $\sim4.4$ and $127 M_\oplus$ (within 5%) can be viewed as
"intermediate-mass" planets, where $R \propto M^{0.67}$. Massive planets, or
gas giant planets, are found to have masses beyond $127 M_\oplus$ with an
$M$-$R$ relation of $R \propto M^{-0.06}$. By analyzing the radius-density
relation we also find that the transition between "small" to
"intermediate-size" planets occurs at a planetary radius of $\sim1.6 R_\oplus$
(within 3%). Our results are consistent with previous studies and provide an
ideal fit for the currently-measured planetary population.
