In search of lost edges: a case study on reconstructing financial networks

Michael Lebacher, Samantha Cook, Nadja Klein and Göran Kauermann

Abstract

In this paper, we review the different methods designed to estimate matrixes from their marginals and potentially exogenous information. This includes a general discussion of the available methodology, which provides edge probabilities and models that are focused on the reconstruction of edge values. Besides summarizing their advantages and shortfalls, we conduct a competitive comparison of the approaches using Society for Worldwide Interbank Financial Telecommunication (SWIFT) MT 103 single customer credit transfers. The comparison concerning the binary reconstruction is divided into an evaluation of the edge probabilities and of the accuracy of the predicted edge values. To test the methods on different topologies, the application is split into two parts. The first part considers the full MT 103 network, providing an illustration of the reconstruction of large, sparse financial networks. The second part is concerned with reconstructing a subset of the full network, representing a dense medium-sized network. Regarding substantial outcomes, it is found that there are some methods that do work well in many respects. However, that does not imply that a certain method is generally superior. In general, the preferred model choice highly depends on the goal of the analysis, the presumed network structure and the availability of exogenous information.