The structure of the typical graphs of given diameter

In this paper it is proved that there are constants 0n−c2lognd>n−c2logn the typical graph has a completely different snakelike structure. The number of nn-vertex graphs of diameter dd is (1+o(1))12n(d+1)3n−d−1dn−d−1 whenever n→∞n→∞ and d>n−c2lognd>n−c2logn.