Using a Social Network and Graph Theory to Find Out the Most Important Character in Game of Thrones (Psst. It’s not Jon or Daenerys)

Many television watchers today are rushing to their TVs or mobile devices every week to indulge in the newest hit show House of the Dragon;  which is the prequel to an even more popular series Game of Thrones which adapts the famous novels of George R. R. Martin. Game of Thrones is an epic fantasy series that takes place in the imaginary continents of Westeros and Essos, and it tells the tale of many noble families using their might, strategy, and even dragons to try and impose their claim on the iron throne to be the next ruler of all the lands west of the Narrow Sea. One would expect that this series was popular because of the thrill and visuals provided by the mythical creatures and large scale battles, which is true, however the main reason this series was as big as it was, is because of the tension and political intrigue that was provided by the well designed characters and their interactions and dialogue between each other. These rich interactions gave us alliances that were formed and betrayals that suddenly occurred, which added a whole new dimension to the show. This also gave us the stories of beloved characters by pushing them to the forefront of the plot, such as Jon Snow and Daenerys Targaryen.

Since the start of the show aside from the factions that we saw on our screens there was always factions within the show’s fanbase that divided fans based on who they were rooting for and who they thought was the true protagonist of the series. Many favourites emerged such as Jon and Daenerys but because of the many rich interactions and storylines an argument can be made for the many characters that were playing the “game” for the throne. So in 2016, Macalester College professor Andrew Beveridge and graduate student Jie Shan created a graph of the social network for the characters in Game of Thrones. They used the novel version of the story, where nodes represented the individual characters and edges and their respective weights were incremented when the characters’ names appeared in the novel within 15 words (helped capture actual interaction and mentions).

As seen above from the social network’s graph it is pretty easy to notice that Tyrion Lannister would be the true protagonist of the series, if we had to pick one. This also makes sense since he is one of the smartest players in the series and many of his schemes start many storylines and impact many characters in the story. However, the visual is not the only thing supporting Tyrion as the most important character. Beveridge and Shan used other graph theory measures (like betweenness from class) that also points to Tyrion being the most important character.

Tyrion was first for both degree and weighted degree measures, meaning he interacted with the highest number of other characters and also had the most number of interactions. He also came first in eigenvector and PageRank measures which enhance the degree measures by also factoring in the importance of the connection. So in this case, connections with more influential characters are given a higher score than other connections. Tyrion being first in these categories means that his interactions were not significant just in quantity but also in quality (interacted with the most nobles and other influential characters that really move the story forward). These measure’s significance is really visible when you look at the character King Robert Baratheon. He passed early on in the story so he didn’t have a lot of interactions (rank 14 in weighted degree), however since he was the King he directly interacted the heads of the various noble families and that means the interactions he had were mostly significant with influential characters (rank 8 in PageRank). Tyrion also came first in closeness (average distance to all other nodes; the lower the better since that means the node is the closest to all other nodes) this means his information and interactions travels the quickest from him to all other characters. The final measure analyzed is betweenness (similar to class), here betweenness of a node is the number of shortest paths this node is part of for other pairs of nodes. Higher rankings in this measure means that the character is important in connecting other characters from other clusters (acting like a bridge). Here Tyrion is actually 3rd, but this is expected as the characters higher than him are Jon Snow who connects the House of Stark and the wildings and the Night’s Watch in the north, and second goes to King Robert who because of his title connects to most of the different noble houses/clusters. However, Tyrion came first in all measures and one 3rd place ranking so he is still the most important character in Game of Thrones by a considerable amount.

Here Andrew Beveridge and Jie Shan were able to apply graph theory on the Game of Thrones’ social network and were able to deduce that Tyrion Lannister as the most important character (real protagonist) of the series and they used various graph measures to analyze the network and back their claim up with both qualitative and quantitative thinking. They also mentioned in their paper that Daenerys was also considerably high in the rankings despite the fact that in the part of the novel they used she was in the other continent of Essos, and this means they were able to see that she would end up showing up in Westeros which actually ended up happening in the show. Graph theory in this context was applied to a fictional world’s social network, but the same ideas can be applied in the real world. Many companies like Facebook already apply these measures to their network which help implement many features such as friend recommendations and others. This type of analysis may also help with future predictions and have other applications based on the context of the network. This is a very powerful way of thinking of the world, whether it is a fantasy world or the real world.

Source:
Beveridge, A., and Shan, J. (2016). Network of Thrones. Math Horizons, 23(4), 18–22. https://doi.org/10.4169/mathhorizons.23.4.18

Used the UTSC library’s link to access the article: https://librarysearch.library.utoronto.ca/permalink/01UTORONTO_INST/fedca1/cdi_crossref_primary_10_4169_mathhorizons_23_4_18