In a wonderful book “Economyths”, the author, David Orrell, applies network theory to the financial crises.

“The banking and electrical systems are two examples of technological networks. Others are the transportation network, the telecommunications network, and the world wide web. Similar networks are ubiquitous in nature: biological systems are characterised by complex networks of interacting genes and proteins, ecosystems by predator-prey relationships. And sociologists use social networks to investigate the transmission of ideas and trends through society.

Researchers in the field of network science view such systems in terms of nodes, which represent individuals or agents in the network, and links, which join the nodes and represent interactions of some kind. In a biological model the nodes could represent proteins or cells; in an ecosystem model they could represent species; in a social network they could represent people; in a model of the electrical grid they could represent power stations or consumers; in a model of the economy they could represent firms. For example, one paper published by Domenico Delli Gatti from the Catholic University of Milan and colleagues in June 2008 observed that: 'The complex pattern of credit relationships is a natural research issue to be dealt with by means of network analysis. It is straightforward to think of agents as nodes and of debt contracts as links in a credit network…. the default of one agent can bring about an avalanche of bankruptcies (their italics)’.If the authors had delayed publication a few months, they could have used Lehman’s example.

Researchers have found that such networks - be they technological, biological, ecological, social, or economic- often have much in common, and can be divided into certain categories. One is the small-world network, where the connections between individual nodes are arranged in such a way that it takes only a small number of steps to link one node to another. The world wide web has this property, and search companies Google exploit it to derive their algorithms. Another category is scale-free networks. The term 'scale-free' means that there is no typical or expected number of connections for any node: most nodes have few connections to other nodes, but a small number of hubs are highly connected. An example is the air traffic net work: some airports such as Heathrow are global hubs, while smaller regional airports may fly to only a few destinations.

Artificial networks with these and other properties can easily be produced and studied on the computer. Network modelling of the economy has become an active research area, in academia and institutions including the Bank of England. One of the key questions that engineers and network scientists are concerned with is network robustness, which often depends strongly on the way in which the network is arranged. Much can be learned from natural systems, such as ecosystems or biological systems, simply because they have been around for a long time so have presumably learned a trick or two. Some ‘design  principles’ shared by robust networks - but not currently by our financial system - include modularity, redundancy, diversity, and a process  for controlled shut-down. Together they provide clues on how we can reduce the chance of another disaster.

Modularity A network's modularity refers to its degree of compartmentalisation. In, for example, a small-world network, each node is connected to any other node by of connections. This is good if the aim is communication, but in other cases it can be a problem. Scientists have studied the spread of epidemics using detailed network models of artificial societies in which nodes represent individuals, and connections between nodes represent the potential spread of the disease from one person to another. It turns out that one of the main factors determining the rate of spread is the transport network - the 2009 swine flu pandemic spread so quickly because of long-distance connections through air travel.

The banking system too has become increasingly integrated, and therefore vulnerable to contagion of a different sort. After the Great Depression, the Glass-Steagall Act was introduced in the- US to separate commercial banks, responsible for day-to-day consumer banking, from investment banks, which were primarily involved in speculation. The repeal of this act in 1999 by the Gramm-Leach-Bliley Act dissolved the wall, and allowed banks like Citigroup to go nuts with derivatives, lose billions, and get rescued by the US government. (The same act also led to deregulation of electricity markets and the Enron saga.) On an international level, the degree of financial connectivity between major markets has increased dramatically in recent decades-meaning that if one catches a cold, they all get it. Complex living organisms, or natural systems such as food webs, tend to be built up of smaller, weakly connected sub-networks, which reduces the probability of contagion from one area to another.

The overall topology or structure of the network architecture is also important. A common motif in biological and engineering networks is the 'bow-tie' structure, in which multiple inputs (one side of the bow) feed into a central control unit (the knot) to produce multiple outputs (the other side of the bow). An example again is the internet, where a wide variety of material such as web pages, emails, video and so on, is first compressed into a homogeneous, standardised computer language before expanding again as output on a user's screen. According to control theorists, who study the control of dynamical systems in engineering, the bow -tie structure has evolved in both natural and man- made systems because it allows a balance between robustness and efficiency. The system is quite efficient, because it uses a standardised language to handle all the diverse inputs and outputs, but at the same time it is easy to monitor events and correct mistakes. In finance the equivalent to a central control module would be a central clearing house for instruments such as derivatives. These are currently often sold over- the- counter, which makes it impossible to measure or control systemic risk.

Redundancy Another trick that nature employs to improve rebustness is keeping something in place for backup. If one node of link in the network fails, another can take its place. The extra kidney fails (or you need to donate one). In financial terms, this supports the idea that banks should retain a higher minimum level of cash reserves, which could be adjusted up for large institutions or investment strategies that pose systemic risk.

Much of the appeal of the complex financial products developed in the last decade is that they enabled financial institutions to get around reserve requirements. Investment banks such as Lehman Brothers were leveraged at extremely high ratios (over 30 to 1), so they were essentially gambling with other people's money. The danger, as chairman of the US Federal Deposit Insurance Corporation Sheila Bair told a conference in June 2007, is that 'Without proper capital regulation, banks can operate the marketplace with little or no capital. And governments and deposit insurers end up holding the bag, bearing much of the risk and cost of failure.... The final bill for inadequate capital regulation can be very heavy. In short, regulators can't leave capital decisions totally to the banks. We wouldn't be doing our jobs or serving the public interest if we did. Canadian banks survived the credit crunch relatively unscathed, in large part because they have tougher lending requirements than their American counterparts.

Diversity A degree of diversity in a system can help it adapt to change. In an ecosystem this equates to a range of species; in the financial system it equates to diversity of trading strategies. On the surface, our financial system would appear to be highly diverse. However, one surprise to come out of the crisis was that everyone appeared to be employing the same strategies. Even adventurous hedge funds, which are supposed to come up with innovative ways to make money, were susceptible to group-think. Intense competition between institutions meant they were afraid of under-performing their peers, so were actually more likely to adopt the same techniques. As one trader put it, they 'talk to each other and have many of the same trades. These are people who say, "I see a pattern, and I've got to jump on.’’’’

The trend was exacerbated by the fact that funds often use quantitative rule-based strategies, which are inherently easy to copy. Banks also adopted near-identical risk models, even though they were known to be flawed, exactly because they were widely accepted by the industry. Complexity scientists are starting to monitor these different strategies, and the relationships between them, in the same way that ecologists monitor species in an ecosystem.

Controlled shut-down When cells in the human body damaged beyond repair - say after exposure to toxins or radiation - they are usually targeted for a form of controlled death known as apoptosis. In this process, the constituents of the cell are taken apart and recycled for use elsewhere in the body. cancer cells, the apoptotic machinery is disabled, and cells at the interior of the tumour become necrotic - they burst, disgorging their contents in a fashion that harms nearby cells.

When Lehman went bankrupt, its death was necrotic rather than apoptotic. In the US alone, it had over a million derivatives transactions outstanding with some 6,500 trading partners. Figuring out the mess will keep hundreds of lawyers employed for years. Banks also often structure themselves in a deliberately labyrinthine manner in order to avoid taxes, which makes them hard to wind up. Proposals for 'living wills' for banks are being considered by institutions including the UK's Financial Services Authority.

To improve the robustness of our financial system it therefore follows that we should increase modularity, redundancy and diversity, and provide a mechanism for controlled shutdown. This applies not just to banks, but to other industries such as agriculture or retail, which, as discussed later, exhibit many of the same problems. There's only one problem: none of these measures would be seen as desirable according to orthodox dogma. The reason is again related to the idea of efficient markets.

Fixing the grid

According to theory, markets are made efficient if each atom (e.g. individual or company) pursues its own self-interest. Here self-interest refers usually to short-term interest, because if a company neglects the short term it will be taken over by competitors. And what happens after it dies is irrelevant. Economics likes to live only in the present.

Companies, including banks, therefore spend a lot of time worrying about their own short-term risk, but much less on systemic risk. Governments and regulatory institutions have also generally gone along with the idea that markets are self-regulating (though after the credit crunch, Alan Greenspan admitted that this idea was 'a flaw in the model... that defines how the world works'). The financial network is therefore allowed to evolve towards a state that appears highly efficient in the short term, but is constantly accumulating systemic risk.

Introducing modularity, for example by separating speculative activities from ordinary commercial banking activities, or dividing large global banks into clearly defined national components, would probably reduce short-term efficiency, as would building extra slack and capacity into the system, e.g. by increasing the amount of money that banks need to keep on reserve. Such measures can therefore be taken only by a strong regulatory agency. Some progress is now being made - there is certainly a desire for reform in the air - but changes will occur only under protest by the banks, which appear to have learned few lessons from the crisis, except that they can rely on taxpayer bail-outs. Indeed with the collapse of many players, the banking industry is more concentrated than it was before the crisis.

It is interesting to ask whether the credit crunch would ever have happened if politicians and risk experts at banks had been trained or educationally shaped in fields like complexity and network theory rather than orthodox economics. When the US government took the decision to let Lehman fail in an uncontrolled manner, it seems that the administration was taken aback by the knock-on effects. It was like an untrained apprentice engineer wandering into the control room and unplugging the thick cable with the 'DO NOT DISCONNECT' sign above it. And the result was nearly lights out for the economy. Three days after Lehman's bankruptcy, on 18 September, the Federal Reserve had to intervene to stop an electronic bank run on US money market accounts. As Representative Paul Kanjorski of Pennsylvania explained, they feared that if it were allowed to continue, '$5.5 trillion would have been drawn out of the money market system of the US, which would have collapsed the entire economy of the US, and within 24 hours the world economy would have collapsed. It would have been the end of our economic system and our political system as we know it.’

The next way to revive economics, then, is to educate our cadre of highly-paid 'financial engineers' in the principles and codes of real engineering. This includes building in firebreaks and safeguards to help prevent systemic failure, and developing diagnostic tools for the collection and analysis of network data. 'At present; notes the Bank of England's Andrew Haldane, 'risk measurement in financial systems is atomistic. Risks are evaluated node by node. In a network, this approach gives little sense of risks to the nodes, much less to the overall system. It risks leaving policymakers navigating in dense fog when assessing the dynamics of the financial system.

Disasters and breakdowns will always occur, but the effects can be minimised and procedures put in place to get the system up and running as quickly as possible (the blackout in the US north-east was repaired in most places in under a day). New ideas and tools from mathematical areas like network theory and complexity can help to frame the problems, test and refine hypotheses, explore and communicate solutions, and motivate changes. As shown by the influence of neoclassical economics, models can have a large effect on the design of financial structure.”