  Farey sequences of irreducible fractions between 0 and 1 can be related to
graph constructions known as Farey graphs. These graphs were first introduced
by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they
have many interesting properties: they are minimally 3-colorable, uniquely
Hamiltonian, maximally outerplanar and perfect. In this paper we introduce a
simple generation method for a Farey graph family, and we study analytically
relevant topological properties: order, size, degree distribution and
correlation, clustering, transitivity, diameter and average distance. We show
that the graphs are a good model for networks associated with some complex
systems.
