The objective of this study is to develop a majorization-based tool to compare financial networks with a focus on the implications of liability concentration. Specifically, we quantify liability concentration by applying the majorization order to the liability matrix that captures the interconnectedness of banks in a financial network. We develop notions of balancing and unbalancing networks to bring out the qualitatively different implications of liability concentration on the system's loss profile. Using both analytical and numerical examples, we illustrate how to identify networks that are balancing or unbalancing, and make connections to interbanking structures identified by empirical research, such as perfect and imperfect tiering schemes. An empirical analysis of the network formed by the banking sectors of eight representative European countries suggests that it is either unbalancing or close to it, persistently over time. We also discuss how our findings support current regulatory policies aiming at limiting the size of gross exposures to individual counterparties.
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