We 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. We illustrate how to identify networks that are balancing or unbalancing, and make connections to interbank structures identified by empirical research, such as tiering schemes. An empirical analysis of the network formed by the banking sectors of eight representative European countries suggests that the system is either unbalancing or close to it, persistently over time. This empirical finding, along with the concentration results, supports regulatory policies aiming at limiting the size of gross exposures toward individual counterparties (joint work with David D.Yao and Peng Chu Chen).