  We present an exact description of a crossover between two different regimes
of simple analogies of small-world networks. Each of the sites chosen with a
probability $p$ from $n$ sites of an ordered system defined on a circle is
connected to all other sites selected in such a way. Every link is of a unit
length. Thus, while $p$ changes from 0 to 1, an averaged shortest distance
between a pair of sites changes from $\bar{\ell} \sim n$ to $\bar{\ell} = 1$.
We find the distribution of the shortest distances $P(\ell)$ and obtain a
scaling form of $\bar{\ell}(p,n)$. In spite of the simplicity of the models
under consideration, the results appear to be surprisingly close to those
obtained numerically for usual small-world networks.
