SAFETY IN NUMBERS

# What math can tell us about the final season of “Game of Thrones”

Most questions on Game of Thrones are answered with the sharp end of a sword. Math and science aren’t nearly as sexy, but numbers have a lot to say about the conclusion of the HBO drama, if only we’d listen.

As HBO prepares to air the final season of Game of Thrones (April 14), everyone is trying to figure out which character will ultimately sit in the Iron Throne. Las Vegas oddsmakers peg Bran Stark as the one most likely to rule Westeros at the conclusion of the final season. Some fans think it’s more likely to be his big sister, Sansa. Others believe that all those contending for the throne will perish in some cataclysm (an allegory for climate change, perhaps?), leaving the seat eternally vacant.

These are all just guesses. Network science, however, provides some concrete ideas about where the show’s final season is trending, based on analysis of seven seasons’ worth of character interactions.

Macalester College professor Andrew J. Beveridge’s research, “Network of Thrones,” uses the field of network science—an interdisciplinary blend of graph theory, computer science, and sociology—to map every relationship in George R.R. Martin’s novels. The network doesn’t necessarily know who will win the throne, but it does tell us who’s mathematically most central to the narrative. The result when we last checked in with him, in 2016? Tyrion Lannister.

Since then, Beveridge has updated his network, applying his research to all seven seasons of the HBO series that have aired. While Tyrion is still the most important when considering the show as a whole, two different characters have emerged as most crucial to the narrative headed into the final season. He explains in our video, above.

The concept behind Beveridge’s network is actually pretty simple. Whenever two characters interact (that includes talking directly, but can also mean just appearing in the same location), a link—called an “edge”—is placed between them. The edges are weighted based on how frequently the two characters interact. Each character is then ranked by five different measures:

• Degree centrality: The number of connections (“edges”) a character has
• Weighted degree centrality: The total number of interactions a character has
• Eigenvector centrality: A measure of connections to important people
• PageRank centrality: A measure of interactions with important people
• Betweenness centrality: The number of short paths that go through a given character (this measures how important one’s position within the network is)

Ranked first in every measure last season—often by a wide margin—is Jon Snow.

Daenerys Targaryen is ranked second in four of the five measures, and third in the other. Tyrion, meanwhile, is beginning to take a backseat, ranked sixth in betweenness and fourth in PageRank (he’s not hanging out with the powerful Lannister clan he was born into as much these days). Still, he remains crucial to the narrative, as he’s an intermediary between Jon and Daenerys.

Ranked fourth overall in betweenness, surprisingly, is Sam Tarly, a supporting character who has suddenly been thrust into the thick of the narrative. He’s the one who discovered the truth of Jon’s parentage and cured Jorah’s greyscale. So don’t be surprised if his ranking increases even more in the final season—the numbers suggest he’s gearing up to play a major role.

And while Jaime Lannister doesn’t have many connections, his strongest one—his sister, Cersei—keeps him ranked high in most measures. The network seems to think that Jaime will have a very important part in how the HBO series concludes.

Correction: The video says that Macalester College is in Minneapolis, Minnesota. It is actually in Saint Paul, Minnesota.

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