  Modelling systems with networks has been a powerful approach to tame the
complexity of several phenomena. Unfortunately, such an approach is often made
difficult by the large number of variables to take into consideration. Methods
of dimensional reduction are useful tools to rescale a complex dynamical
network down to a low-dimensional effective system and thus to capture the
global features of the dynamics. Here we study the application of the
degree-weighted and spectral reduction methods to an important class of
dynamical processes on networks: the propagation of credit shocks within an
interbank network, modelled according to the DebtRank algorithm. In particular
we introduce an effective version of the dynamics, characterised by functions
with continuous derivatives that can be handled by the dimensional reduction.
We test the reduction methods against the full dynamical system in different
interbank market settings: homogeneous and heterogeneous networks generated
from state-of-the-art reconstruction methods as well as networks derived from
empirical e-MID data. Our results indicate that, for proper choices of the bank
default probability, reduction methods are able to provide reliable estimates
of systemic risk in the market, with the spectral reduction better handling
heterogeneous networks. Finally we provide new physical insights on the nature
and working principles of dimensional reduction methods.
