The diversity vector of balls of a typical graph of small diameter

For ordinary connected graphs, the diversity vectors of balls ($i$th component of the vector is equal to the number of different balls of radius $i$) are studied asymptotically. The asymptotic behavior of the number of graphs of small diameter with full diversity of balls is investigated. The diversity vector of balls of a typical graph of the given small diameter is calculated. Asymptotically exact value of the number of labeled $n$-vertex graphs of diameter 3 is obtained. Ill. 2, bibliogr. 12.