Document Type

Research Report

Publication Date



Santa Fe Institute


The financial crisis of 2007-2009 demonstrated the need to understand the macrodynamics of interconnected financial systems. A fruitful approach to this problem regards financial infrastructures as weighted directed networks, with banks as nodes and loans as links. Using a simple banking model in which banks are linked through interbank lending, with an exogenous shock applied to a single bank, we find a closedform analytical solution for the degree at which failures begin to propagate in the network. This critical degree is expressed as a function of four financial parameters: banking leverage; interbank exposure; return on the investment opportunity; and interbank lending rate. While the transition to failure propagation is sharpest with regular networks, we observe it numerically for random and scale-free networks as well. We find that, if the expected number of failures is not strongly dependent on the network topology and is well captured by the notion of critical degree, the frequency of catastrophic cascades (with a single shock inducing all or most banks in the network to fail) tends to be much larger on scale-free networks than on classical random networks. We interpret this finding as a manifestation of the “robust-yet-fragile” property of scale-free networks.


Reprinted with permission.



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