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## University of Groningen

Skip to 0 minutes and 10 secondsComplex systems can often be depicted or modelled as networks. The mathematical tool for network analysis is graph theory. It's basic tools are nodes and edges. In this lecture, we deal with the stability, resilience, and sustainability of networks.

Skip to 0 minutes and 31 secondsThe stability of the network is an important issue in physics, IT, biology, and also in social networks, of course, in the economy as well. There are two views off stability or instability. The first view is the shock and propagation theory. This theory can be analysed with graph theory. Shocks are propagated through so-called cascade. The shock, as it were, travel through the network. And questions come up like, does the cascade stop and when? Or does it destroy the complete network? And that can be analysed in the network framework. The robustness or stability depends on the diversity of the nodes, their degree of interconnectedness, and buffers in individual nodes, and also in the interaction of these factors in a nontrivial way.

Skip to 1 minute and 27 secondsThe size of shocks is important, and also the issue of whether they are common. That means that they affect all or a great number of nodes.

Skip to 1 minute and 39 secondsStress tests can be conducted to assess the stability of the network, and also so-called reverse stress tests. In a reverse stress test, we try to find out how we can break down the network and let it fall apart. In a stress test, we just add a shock and see what happens in the network as a whole.

Skip to 2 minutes and 2 secondsSo the first theory is shock and then propagation. The second theory about instability says that vulnerability in a network builds up from within and over time. That's what we call an endogenous process. So it's inherent in the network. It's inherent in the system. And it's not driven primarily by exogenous shocks. Exogenous shocks are shocks from the outside. So it builds up internally. And after some time, very little is needed to destabilise the network or cause it's complete collapse.

Skip to 2 minutes and 42 secondsSudden transition from a stable network to instability. That's what can happen in such an endogenous theory of instability.

Skip to 2 minutes and 54 secondsThe recent financial crisis is a good example. This will be discussed later in this course.

Skip to 3 minutes and 2 secondsNotion of systemic risk is important when we look at the stability of a network. A systemic risk is the probability that the structure or pattern that is in the system will collapse. We call a network stable, robust, or resilient if that network is able to absorb large shocks and does not build up fragility from within. And by fragility, we mean the vulnerability of the network to shocks from the outside, to an external shocks. So we discussed two theories, an endogenous theory of instability and the exogenous theory of instability, the shock propagation theory and the endogenous theory of instability. Both theories are complementary. You can use them in one framework.

Skip to 3 minutes and 57 secondsAnd graph theory is a powerful tool to analyse policies and regulations for making a network more stable. For instance, you can analyse whether a financial system will become more stable if you kept the size of the banks in that system, or if you make a distinction between investment banks and retail banks, and whether you have central clearing of derivatives. And all kinds of structural issues can be analysed in graph theory and can be analysed whether they will make the financial system stable, or perhaps even more unstable. In this lecture, we have looked at the instability or stability of networks. Two theories of instability were discussed.

Skip to 4 minutes and 45 secondsAnd a number of notions related to this issue were discussed, such as systemic risk, fragility, and stress testing, and reverse stress testing.

# Stability of networks

This lecture gives a short overview of stability of networks.

Networks can break down. This might happen because of outside shocks but networks can also built up internal instability over time. In academia we refer to the first as shock propagation theory and the second as the theory of endogenous vulnerability. There are several ways of increasing both network stability and resilience such as increasing buffers or decreasing connections.

In another extra step at the end of this activity we show you a way to perform a reverse stress test on the network of internet trackers from the previous extra step.