Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we construct networks of European banks and demonstrate that the latent geometry of these financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. Using two different hyperbolic embedding methods, hydra+ and Mercator, this allows us to connect the network structure to the popularity-vs-similarity model of Papdopoulos et al., which is based on the Poincaré disc model of hyperbolic geometry. We show that the latent dimensions of ‘popularity’ and ‘similarity’ in this model are strongly associated to systemic importance and to geographic subdivisions of the banking system, independent of the embedding method that is used. In a longitudinal analysis over the time span from 2014 to 2018 we find that the systemic importance of individual banks has remained rather stable, while the peripheral community structure exhibits more (but still moderate) variability. Based on our analysis we argue that embeddings into hyperbolic geometry can be used to monitor structural change in financial networks and are able to distinguish between changes in systemic relevance and other (peripheral) structural changes.

基于2014年，2016年欧洲银行业压力测试和2018年透明度工作的数据，我们构建了欧洲银行网络，并证明了这些金融网络的潜在几何形状可以很好地表示为负曲率几何形状，即双曲线。几何学。使用hydra +和Mercator两种不同的双曲嵌入方法，这使我们能够将网络结构连接到Papdopoulos等人的基于相似度的Poincaré圆盘模型的Popularity-vs-likeness模型。我们表明，在此模型中，“人气”和“相似性”的潜在维度与系统重要性和银行系统的地理细分密切相关，而与所使用的嵌入方法无关。在2014年至2018年的时间跨度的纵向分析中，我们发现单个银行的系统重要性一直保持稳定，而外围社区结构表现出更多（但仍为中等）的可变性。根据我们的分析，我们认为嵌入双曲线几何可用于监视金融网络的结构变化，并且能够区分系统相关性变化和其他（外围）结构变化。