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.

遇险传播发生在连接的网络中，其速率和范围取决于网络拓扑。为了对此进行研究，我们选择经济生产网络作为范例。一个经济网络可以在多个层面上进行检验，即个体之间的联系（微观），企业/部门之间的联系（微观）或国家之间的联系（宏观）。新的紧急动力学特性出现在每个级别，因此粒度很重要。对于病毒性流行病，即使是单个节点也可能成为困扰的中心，并可能影响整个网络。但是，众所周知，经济网络在微观层次上是免疫的，在中观/宏观层次上更容易失败。我们提出了一个动态交互模型来描述遇险传播的机制，该机制在不同震中发起，跨越网络的不同模块。脆弱的模块通常会导致很大程度的不稳定。我们使用独特的经验数据集展示了我们的方法，该数据集涉及印度一个行政州（一个发展中的经济体）中14万家公司的投入产出关联。该网络具有多个轮辐结构，这些结构表现出适度的分散性，随粗粒度水平而变化。新颖之处在于在不同级别的粒度或模块化下表征生产网络，并发现在遇险传播中“太大到失败”模块取代了“太中心到失败”模块。该网络具有多个轮辐结构，这些结构表现出适度的分散性，随粗粒度水平而变化。新颖之处在于在不同级别的粒度或模块化下表征生产网络，并发现在遇险传播中“太大到失败”模块取代了“太中心到失败”模块。该网络具有多个轮辐结构，这些结构表现出适度的分散性，随粗粒度水平而变化。新颖之处在于在不同级别的粒度或模块化下表征生产网络，并发现在遇险传播中“太大到失败”模块取代了“太中心到失败”模块。