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Distress propagation occurs in connected networks, its rate and extent beingdependent on network topology. To study this, we choose economic productionnetworks 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 dynamicalproperties appear at every level, so the granularity matters. For viralepidemics, even an individual node may act as an epicenter of distress andpotentially affect the entire network. Economic networks, however, are known tobe immune at the micro-levels and more prone to failure in themeso/macro-levels. We propose a dynamical interaction model to characterize themechanism of distress propagation, across different modules of a network,initiated at different epicenters. Vulnerable modules often lead to largedegrees of destabilization. We demonstrate our methodology using a uniqueempirical data-set of input-output linkages across 0.14 million firms in oneadministrative state of India, a developing economy. The network has multiplehub-and-spoke structures that exhibits moderate disassortativity, which varieswith the level of coarse-graining. The novelty lies in characterizing theproduction network at different levels of granularity or modularity, andfinding `too-big-to-fail' modules supersede `too-central-to-fail' modules indistress propagation.

Distress propagation on production networks: Coarse-graining and modularity of linkages