The Hyperbolic Geometry of Financial Networks

9 Pages Posted: 1 Jun 2020

See all articles by Martin Keller-Ressel

Martin Keller-Ressel

Dresden University of Technology - Department of Mathematics

Stephanie Nargang

TU Dresden

Date Written: April 30, 2020


Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. 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. 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.

Keywords: financial network, network geometry, hyperbolic geometry, systemic risk, financial contagion

JEL Classification: C65, G21

Suggested Citation

Keller-Ressel, Martin and Nargang, Stephanie, The Hyperbolic Geometry of Financial Networks (April 30, 2020). Available at SSRN: or

Martin Keller-Ressel (Contact Author)

Dresden University of Technology - Department of Mathematics ( email )

Zellescher Weg 12-14
Willers-Bau C 112
Dresden, 01062

Stephanie Nargang

TU Dresden ( email )

Münchner Platz 2 - 3
Dresden, 01069

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