2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134651We apply a theorem of Wick to rewrite certain classes of exponential measures on random graphs as integrals of Feynman-Gibbs type, on the real line. The analytic properties of these measures can then be studied in terms of phase transitions; spaces of scale-free trees are a particularly interesting example.One background technical issue is that graphs up to isomorphism are a kind of moduli space, which has orbifold points, whose symmetries make counting delicate. Revised, to correct a reprehensible sign error; references updatedStatistical MechanicsSoft Condensed MatterCombinatoricsMolecular Networks05Cxx, 81Q30text