  We revisit the mass-size relation of molecular cloud structures based on the
column density map of the Cygnus-X molecular cloud complex. We extract 135
column density peaks in Cygnus-X and analyze the column density distributions
around these peaks. The averaged column density profiles, $N(R)$, around all
the peaks can be well fitted with broken power-laws, which are described by an
inner power-law index $n$, outer power-law index $m$, and the radius $R_{\rm
TP}$ and column density $N_{\rm TP}$ at the transition point. We then explore
the $M-R$ relation with different samples of cloud structures by varying the
$N(R)$ parameters and the column density threshold, $N_0$, which determines the
boundary of a cloud structure. We find that only when $N_0$ has a wide range of
values, the $M - R$ relation may largely probe the density distribution, and
the fitted power-law index of the $M-R$ relation is related to the power-law
index of $N(R)$. On the contrary, with a constant $N_0$, the $M - R$ relation
has no direct connection with the density distribution; in this case, the
fitted power-law index of the $M - R$ relation is equal to 2 (when $N_0\ge
N_{\rm TP}$ and $n$ has a narrow range of values), larger than 2 (when $N_0\ge
N_{\rm TP}$ and $n$ has a wide range of values), or slightly less than 2 (when
$N_0< N_{\rm TP}$).
