In this paper, we find recursive formulas for the Tutte polynomial of a
family of small-world networks: Farey graphs, which are modular and have an
exponential degree hierarchy. Then, making use of these formulas, we determine
the number of spanning trees, as well as the number of connected spanning
subgraphs. Furthermore, we also derive exact expressions for the chromatic
polynomial and the reliability polynomial of these graphs.Comment: 6 page
