  We consider a model of contagion in financial networks recently introduced in
the literature, and we characterize the effect of a few features empirically
observed in real networks on the stability of the system. Notably, we consider
the effect of heterogeneous degree distributions, heterogeneous balance sheet
size and degree correlations between banks. We study the probability of
contagion conditional on the failure of a random bank, the most connected bank
and the biggest bank, and we consider the effect of targeted policies aimed at
increasing the capital requirements of a few banks with high connectivity or
big balance sheets. Networks with heterogeneous degree distributions are shown
to be more resilient to contagion triggered by the failure of a random bank,
but more fragile with respect to contagion triggered by the failure of highly
connected nodes. A power law distribution of balance sheet size is shown to
induce an inefficient diversification that makes the system more prone to
contagion events. A targeted policy aimed at reinforcing the stability of the
biggest banks is shown to improve the stability of the system in the regime of
high average degree. Finally, disassortative mixing, such as that observed in
real banking networks, is shown to enhance the stability of the system.
