Early-warning signals of the 2008 crisis in the Dutch interbank network.

Early-warning signals of the 2008 crisis in the Dutch interbank network.

The figure portrays a temporal analysis of two loops, pairs of banks that are at the same time debtor and creditor to each other. Although the raw number of two loops is not very informative about possible ongoing structural changes, its comparison with a random network model benchmark is. A z-score represents the number of standard deviations by which the number of two loops in the real network deviates from its expected value in the model. Small magnitude z-scores (<3) indicate approximate consistency with the model, whereas larger magnitudes indicate statistically significant deviations.

Two different random network models were used: a homogeneous network with the same total number of links as in the real network (top) and a heterogeneous network where every bank has the same number of connections as in the real network (bottom). The homogeneous model, often used in standard analyses, highlights only a late and abrupt structural change (2008). The more realistic heterogeneous model also identifies a gradual, early-warning “precrisis” phase (2005–2007). ^[1]

File:Anticipating Critical Transitions .pdf File:Complexity theory and financial regulation.pdf

Complexity theory and financial regulation Science ^[2]

Tiziano Squartini, Iman van Lelyveld & Diego Garlaschelli Early-warning signals of topological collapse in interbank networks Scientific Reports 3, Article number: 3357 (2013) doi:10.1038/srep03357

↑ Stefano Battiston1,*, J. Doyne Farmer2,3, Andreas Flache4, Diego Garlaschelli5, Andrew G. Haldane6, Hans Heesterbeek7, Cars Hommes8,9,†, Carlo Jaeger10,11,12, Robert May13, Marten Scheffer14 Complexity theory and financial regulation Science 19 Feb 2016: Vol. 351, Issue 6275, pp. 818-819 DOI: 10.1126/science.aad0299