  We propose a consistent approach to the statistics of the shortest paths in
random graphs with a given degree distribution. This approach goes further than
a usual tree ansatz and rigorously accounts for loops in a network. We
calculate the distribution of shortest-path lengths (intervertex distances) in
these networks and a number of related characteristics for the networks with
various degree distributions. We show that in the large network limit this
extremely narrow intervertex distance distribution has a finite width while the
mean intervertex distance grows with the size of a network. The size dependence
of the mean intervertex distance is discussed in various situations.
