  Distress propagation occurs in connected networks, its rate and extent being
dependent on network topology. To study this, we choose economic production
networks as a paradigm. An economic network can be examined at many levels:
linkages among individual agents (microscopic), among firms/sectors
(mesoscopic) or among countries (macroscopic). New emergent dynamical
properties appear at every level, so the granularity matters. For viral
epidemics, even an individual node may act as an epicenter of distress and
potentially affect the entire network. Economic networks, however, are known to
be immune at the micro-levels and more prone to failure in the
meso/macro-levels. We propose a dynamical interaction model to characterize the
mechanism of distress propagation, across different modules of a network,
initiated at different epicenters. Vulnerable modules often lead to large
degrees of destabilization. We demonstrate our methodology using a unique
empirical data-set of input-output linkages across 0.14 million firms in one
administrative state of India, a developing economy. The network has multiple
hub-and-spoke structures that exhibits moderate disassortativity, which varies
with the level of coarse-graining. The novelty lies in characterizing the
production network at different levels of granularity or modularity, and
finding `too-big-to-fail' modules supersede `too-central-to-fail' modules in
distress propagation.
