  We consider the (unoriented) long-range percolation on Z^d in dimensions
d\ge1, where distinct sites x,y\in Z^d get connected with probability
p_{xy}\in[0,1]. Assuming p_{xy}=|x-y|^{-s+o(1)} as |x-y|\to\infty, where s>0
and |\cdot| is a norm distance on Z^d, and supposing that the resulting random
graph contains an infinite connected component C_{\infty}, we let D(x,y) be the
graph distance between x and y measured on C_{\infty}. Our main result is that,
for s\in(d,2d), D(x,y)=(\log|x-y|)^{\Delta+o(1)},\qquad x,y\in C_{\infty},
|x-y|\to\infty, where \Delta^{-1} is the binary logarithm of 2d/s and o(1) is a
quantity tending to zero in probability as |x-y|\to\infty. Besides its interest
for general percolation theory, this result sheds some light on a question that
has recently surfaced in the context of ``small-world'' phenomena. As part of
the proof we also establish tight bounds on the probability that the largest
connected component in a finite box contains a positive fraction of all sites
in the box.
