  We investigate the credit risk model defined in Hatchett & K\"{u}hn under
more general assumptions, in particular using a general degree distribution for
sparse graphs. Expanding upon earlier results, we show that the model is
exactly solvable in the $N\rightarrow \infty$ limit and demonstrate that the
exact solution is described by the message-passing approach outlined by Karrer
and Newman, generalized to include heterogeneous agents and couplings. We
provide comparisons with simulations of graph ensembles with power-law degree
distributions.
