Applying network science to current developments: With the election of Trump, Al-Qaeda achieved its objective


In this article, I apply insights in the relationships between network topology and ‘error and attack’ tolerance of networks to the dynamics of the System.

The (current) decoupling (disconnecting) of the United States from the international order can be interpreted as a response to the attack of Al-Qaeda on the WTC in New York, September 11, 2001.

The attack has set in motion – and has shaped – a series of responses from the United States (an attack on the Taliban in Afghanistan in 2001, an attack on Iraq in 2003, etc.) and events that then followed (the Arab Spring, the collapse of states in the Middle East, terrorist attacks, the fragmentation of Europe).

Despite the efforts of president Obama of the United States (2008-2016), the United states – as the most central and dominant state in the international network – was not able to maintain its own and the System’s stability and coherence.

In response, the United States in 2016 (under president Trump) de facto ‘decoupled‘ from the international order, in efforts to promote its own – now narrowly defined – interests (America First).

Insights in network dynamics help explain (from a network perspective) what the impact is on the stability of the (global) System when the United States disengages – decouples – from the international order.

Not surprisingly, the decoupling causes the fragmentation of the international order, and consequently states and radical communities will intensify their efforts to shape local and regional issues in accordance with their own interests as well (and by doing so, confirm Trump’s self fulfilling prophecy).

In this article, I explain the impact of the ‘decoupling’ of the United States from the international order from a network perspective.

As is the case with other networks, the ‘wiring’ (network structure) of the System – the network of communities, including states – to a high degree determines its dynamics, including what is referred to as its ‘error and attack tolerance’. Error and attack tolerance of a network refers to the ability of a network to tolerate attacks; to maintain its stability and ensure its functioning.

Research shows, that many complex systems display a surprising degree of tolerance against errors. This also is the case with the System: Despite regular non-systemic wars and periodic upgrades, the stability of the System – international orders – is relatively great.

In a study Albert et al. observe that “error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the world-wide-web, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network’s connectivity)”.

Albert et al. explain that “the existing empirical and theoretical results indicate that complex networks can be divided into two major classes based on their connectivity distribution P(k), giving the probability that a node in the network is connected to k other nodes. The first class of networks is characterized by a P(k) that peaks at an average” (…) “leading to a fairly homogeneous network, in which each node has approximately the same number of links”.


Visual illustration of the difference between an exponential and a scale-free network. a, The exponential network is homogeneous: most nodes have approximately the same number of links. b, The scale-free network is inhomogeneous: the majority of the nodes have one or two links but a few nodes have a large number of links, guaranteeing that the system is fully connected. Red, the five nodes with the highest number of links; green, their first neighbours. Although in the exponential network only 27% of the nodes are reached by the five most connected nodes, in the scale-free network more than 60% are reached, demonstrating the importance of the connected nodes in the scale-free network. Both networks contain 130 nodes and 215 links.

“In contrast, results on the world-wide web, the Internet and other large networks indicate that many systems belong to a class of inhomogeneous networks, called scale-free networks, for which P(k) decays as a power-law, which are free of a characteristic scale”.

“Whereas the probability that a node has a very large number of connections is practically prohibited in exponential networks, highly connected nodes are statistically significant in scale-free networks”.

Albert et al. have researched the robustness of both types of networks (their ability to absorb disruptions (including attacks in case of the international), without causing instability and a systemic failure in the (functioning) of the network (in the international order in case of the System). The ‘wiring’ of a network is key to understanding its behaviour, including its attack tolerance and stability.

States can be considered nodes in a network of relationships that are ‘embedded’ in an international order. I assume that the more powerful and influential a state is, the more – better – connected the state is in the international order (and vice versa). I assume – because of the United States’ centrality – that the US is the most interconnected node (sate) in the network (international order).

My research and other research show that the network of states resembles a scale-free network.

Albert et al. explain that the robustness of scale-free networks for random attacks – including of the international order (the System), I argue – is much greater than of more homogenous networks: “This robustness of scale-free networks (like the international order, IP) is rooted in their extremely inhomogeneous connectivity distribution: because the power-law distribution implies that the majority of nodes (states in the System, IP) have only a few links, nodes with small connectivity will be selected with much higher probability. The removal of these ‘small’ nodes (small states, IP) does not alter the path structure of the remaining nodes, and thus has no impact on the overall network topology.

If a rocket is randomly fired ‘at’ the international order, the probability that a state with a small connectivity is hit, is much larger than for example the US – a highly connected node – is hit, for the simple reason that there are many more sparsely connected states (nodes) in the international order (network), than highly connected states (nodes).

This characteristic of scale-free networks  – including the System – makes them less vulnerable for random attacks. However, for a targeted attack – a deliberate attack on the most interconnected node (the United States in case of the international order) – the vulnerability of a scale-free network becomes evident: “This vulnerability to attacks is rooted in the inhomogeneity of the connectivity distribution: the connectivity is maintained by a few highly connected nodes (Great Powers in general, and the United States in particular in the current international order, IP) whose removal drastically alters the network’s topology, and decreases the ability of the remaining nodes to communicate with each other.

Albert et al. conclude that “the topological weaknesses of the current communication networks (for scale-free networks in general, including the international order, IP), rooted in their inhomogeneous connectivity distribution, seriously reduce their attack survivability. This could be exploited by those seeking to damage these systems”.

By attacking the United States, Bin Laden chose the most vulnerable node in the network. In response to the events that were set in motion, and the pressure that was consequently ‘put’ on the United States (internally as well as externally) – Trump – a ‘product’ of these events and dynamics – chose to decouple from the international order.

By decoupling, the topology of the international order and the ability of the remaining nodes to communicate with each other and to contribute to the order’s coherence, are drastically decreased.

With the election of president Trump, Bin Laden has achieved his goal: the fragmentation of the international order, the creation of chaos and of more favourable conditions for the exploitation of radical ideas.