Network of Thrones

* Spoilers to follow about Game of Thrones Seasons 1 and 2 *

With Season 6 of Game of Thrones premiering on April 24th, the excitement around the show has once again begun to build. Despite the series’ wild popularity, the series is known for killing off many of the most popular characters. Due to the unpredictable nature of the series, it has been highly debated whether there is a main character in Game of Thrones.

To address this issue, mathematicians Andrew Beveridge and Jie Shan created a social network containing Game of Thrones characters. The social network, which was published in Math Horizons, contains 107 characters (represented by nodes). In order to show the relationship between the characters, 353 integer-weighted edges connect the nodes, with higher weights corresponding to stronger relationships between the characters. The weight of an edge was increased by one every time two characters were mentioned within 15 words of one another. These nodes and edges were generated using the third book of the series, A Storm of Swords, and were laid out geographically. The below graph shows have complex social networks are everywhere in our world. Screen Shot 2016-04-07 at 11.24.47 AM


In order to detect communities in the graph, Beveridge and Shan used the Louvain method to optimize the modularity of the graph. After running the algorithm, seven communities were returned. It is important to note seven distinct communities was an output of the algorithm, rather than an input. These seven communities corresponded to the Lannisters and King’s Landing, Robb’s army, Bran and friends, Arya and companions, Jon Snow and the far North, Stannis’s forces, and Daenerys and her group in Essos. All seven of these communities play a key role in the Game of Thrones series and the authenticity of these communities is confirmed by their separation in the book itself. Although Beveridge and Shan could have done their centrality analysis without having communities, the fact that seven distinct communities were returned shows the accurateness of their process in gathering the data and creating the graph.

With the communities established, Beveridge and Shan used six different centrality measures to determine who the most important characters were, as seen below. First they applied degree centrality, which measures the number of edges incident to a node, to the graph and found that Tyrion Lannister ranked first, with Jon Snow and Sansa Stark tied for second. When weighted degree centrality, which measures the sum of the weights of the edges incident to a node, was applied to the graph, Tyrion Lannister again was ranked first, with Jon Snow in second and Sansa Stark in third. These simply measurements gives the study a baseline that the more advanced measurements can be compared to.

Screen Shot 2016-04-07 at 1.27.13 PM.png

Next, Beveridge and Shan applied more complex centrality measurement to the graph. Eigenvector centrality is similar to weighted degree centrality, but is distinguished by its feedback loop that rewards nodes for being connected to important nodes. Tyrion Lannister was again ranked first, followed by Sansa Stark in second and Jaime Lannister in third. All three of these characters travel during the third book and interact with many of the other major characters, which accounts for their high ranking. Along with this, major characters like Daenerys were ranked relatively low due to their isolation from other major characters. Next, PageRank, the algorithm used by Google Search, was applied to the graph. The advantage of PageRank is that it assigns nodes an inherent importance and the influence of a node is divided up evenly over its connected nodes. While Tyrion Lannister, Jon Snow, and Sansa Stark were first, second, and third, the biggest difference is the change in major characters that were isolated from the pack. For instance, Daenerys jumped to 5th place under PageRank.

Finally, Beveridge and Shan applied two network theories of closeness centrality and betweenness centrality to the graph. Closeness centrality is the average distance, which we discussed in class, from a node to all other nodes. It is not surprising that Tryion and Sansa placed first and second in this ranking, but Robert Baratheon placed third. Although he was one of the least mentioned major characters, his position as King made him a popular topic among many of the major characters in different communities, which intern reduces the average distance to most characters. As discussed in class, betweenness centrality is a measurement of how frequently a node lies on the shortest path between other nodes. The application of this measurement to the graph created very different results compared to the other measurements. For this measurement, Jon Snow ranked first, followed by Robert Baratheon in second and Tyrion Lannister in third. Betweeness centrality rewards those who have many connections outside of their community, as most communication between others in the communities would most likely go through them.

Taking all six centrality measurements into account, Beveridge and Shan conclude that Tyrion is the “main character” of Game of Thrones, followed by Jon Snow and Sansa Stark. With such a complex plot line, it is difficult to definitively name someone a main character, but Beveridge and Shan do an expert analysis of the “Network of Thrones” and show why it is important to use different measurements based on situational factors. Overall, this analysis shows how social networks and present in ever human interaction, whether fact or fiction, and even if a network looks to complex, there are usually underlying communities and sub-communities waiting to be found.

“Network of Thrones”, Math Horizons, Mathematical Association of America, April 2016

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