  We study independent long-range percolation on $\mathbb{Z}^d$ where the
vertices $u$ and $v$ are connected with probability 1 for $\|u-v\|_\infty=1$
and with probability $1-e^{-\beta \int_{u+\left[0,1\right)^d}
\int_{u+\left[0,1\right)^d} \frac{1}{\|x-y\|^{2d}} d x d y } \approx
\frac{\beta}{\|u-v\|^{2d}}$ for $\|u-v\|_\infty\geq 2$, where $\beta \geq 0$ is
a parameter. There exists an exponent $\theta=\theta(\beta) \in
\left(0,1\right]$ such that the graph distance between the origin $\mathbf{0}$
and $v \in \mathbb{Z}^d$ scales like $\|v\|^{\theta}$. We prove that this
exponent $\theta(\beta)$ is continuous and strictly decreasing as a function in
$\beta$. Furthermore, we show that $\theta(\beta)=1-\beta+o(\beta)$ for small
$\beta$ in dimension $d=1$.
