Complex networks & Game of Thrones

Game of thrones is undoubtedly a series of success. 
But what makes it so special? Is there something that makes it different to other TV shows, and so attractive?
I will not answer those questions here. What I am going to talk about is a recent work carried out by Diambo Liu and Luca Albergante, from MIT and the University of Dundee. In this article they have applied the theory of networks to understand the success of the series and see what parameters are important to make the chapters appealing, so that people are looking forward to the following one

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Network theory
Each one of us interacts with other people around us. Family, friends, coworkers, neighbors. Each of the people we interact with in turn do so with other people. In this case each person is the node or vertex of a network, and each relationship is a link of the network. We interact with different intensity with different people, so each link has different strength.

Network theory studies the connections that are created between different nodes, and how they evolve over time. This way, knowing the details of the network, we can understand how it works, or what factors can make it change radically, or if the fact of removing a particular node from the network, will affect drastically the functionality.

Important examples of networks are the brain, where the nodes are the neurons, social networks, air traffic, where the nodes are the airports, the power grid networks.

The researchers of this study have created a network where each node is a family or house of the series: the Lannister, the Stark, the Bolton, the Tyrell, the Targerian. This with all the houses and  all the important groups , such as the Nights Watch or the Iron Bank.

Obviously, the importance of each house is directly related to the number of connections it has.

The Game of Thrones network has a certain similarity with certain marine networks. Where there are minor entities gravitating around a few entities of greater importance. Here would be the Lannister and the Stark. Although it is different from the network of scientific collaborations.

Next they have studied what kind of connections, if friendly or hostile, are between each node, and how those connections evolve, either because of changes in the alliances, because some of the nodes cease to exist, or because two nodes without interaction at first they start to interact.

They have seen that the triads are a very important subgroup. These triads are formed by three nodes and, depending on the mutual relationship (friendly or hostile), the triad may be in balance or umbalanced.

For example, suppose that the Lannister and the Stark are enemies, that the Greyjoy and the Stark get along and the Lannister and the Greyjoy are enemies. This triad is in balance. My friend's enemies are my enemies.

But things can change. For example,  the Greyjoy can become friends with the Lannisters. So, the friends of my friends are my enemies and the balance is lost.

In real political networks, it is believed that there is a tendency to make moves to minimize unbalanced triads. But that is not what happens in Game of Thrones. The fact that the balance is broken allows the series to evolve ... or maybe it breaks so to evolve.

It turns out that these changes are related to those chapters better rated by the audience and that have better acceptance, in the sense of captivating the attention.

The researchers quantify the unpredictability of the series. They use the expression,

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where T3 is a triad of type 3 (2 red links and 1 blue link), and T2 (1 red links and 2 blue link) is a triad of type 2. The denominator is the sum of all the possible triads.

According to the above, the authors claim they can predict the success of each chapter.

In any case, a series of success, which not only allows us to have a good time in front of the screen, but also to talk about science.
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May Science be with you!