  We investigate the finite size corrections to the equilibrium magnetization
of an Ising model on a random graph with $N$ nodes and $N^{\gamma}$ edges, with
$1 < \gamma \leq 2$. By conveniently rescaling the coupling constant, the free
energy is made extensive. As expected, the system displays a phase transition
of the mean-field type for all the considered values of $\gamma$ at the
transition temperature of the fully connected Curie-Weiss model. Finite size
corrections are investigated for different values of the parameter $\gamma$,
using two different approaches: a replica-based finite $N$ expansion, and a
cavity method. Numerical simulations are compared with theoretical predictions.
The cavity based analysis is shown to agree better with numerics.
