  We consider a dynamical model of distress propagation on complex networks,
which we apply to the study of financial contagion in networks of banks
connected to each other by direct exposures. The model that we consider is an
extension of the DebtRank algorithm, recently introduced in the literature. The
mechanics of distress propagation is very simple: When a bank suffers a loss,
distress propagates to its creditors, who in turn suffer losses, and so on. The
original DebtRank assumes that losses are propagated linearly between connected
banks. Here we relax this assumption and introduce a one-parameter family of
non-linear propagation functions. As a case study, we apply this algorithm to a
data-set of 183 European banks, and we study how the stability of the system
depends on the non-linearity parameter under different stress-test scenarios.
We find that the system is characterized by a transition between a regime where
small shocks can be amplified and a regime where shocks do not propagate, and
that the overall stability of the system increases between 2008 and 2013.
