Westeros has no prom king or prom queen, nor does it have a Most Likely to Succeed. But even without the approval of peers — or even social networks like Twitter and Facebook — there is a way to measure importance. And the mathematicians who have, have determined the most important person in Westeros and Essos is Tyrion Lannister.
Using network science, researchers Andrew Beveridge and Jie Shan mapped the 107 characters mentioned in George R.R. Martin's A Storm of Swords and found they were connected to each other in 353 ways. Then, they studied how strong those connections were to each other. Tyrion is the most important character in every way to determine importance - -in all ways, that is, except one. In that case (“betweenness centrality”), he’s beat out by Jon Snow and…the late Robert Baratheon.
Beveridge and Shan state in their paper, entitled "Network of Thrones," what many of us have already known: “Acting as the Hand of the King, Tyrion is thrust into the center of the political machinations of the capitol city. Our analysis suggests that he is the true protagonist of the book.”
The second and third most “important” characters, mathematically speaking? Jon Snow and Sansa Stark, respectively.
The authors seemed surprised at Sansa’s prominence. However, as the heir to the North, she’s a player in her own right — if she decides to play the game of thrones.
Beverage and Shan’s math is too dense for most mere mortals/non-statisticians to understand. But you can see their work for yourselves here.