  We present analytical results for the distribution of shortest path lengths
between random pairs of nodes in configuration model networks. The results,
which are based on recursion equations, are shown to be in good agreement with
numerical simulations for networks with degenerate, binomial and power-law
degree distributions. The mean, mode and variance of the distribution of
shortest path lengths are also evaluated. These results provide expressions for
central measures and dispersion measures of the distribution of shortest path
lengths in terms of moments of the degree distribution, illuminating the
connection between the two distributions.
