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Table of contents

Ultimately, Tyrion is the big winner here. He has close ties to both Lannisters and Starks. This flexibility launches him ahead of his twin siblings. Characters with high betweenness centrality help to connect different parts of the network. These characters provide the narrative glue that binds the story together. They provide efficient pathways for communication and exchange.

Jon Snow has the highest betweenness centrality. Here are the rankings for the top performers:. The well-traveled Tyrion comes in second place.

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He is crucial for connecting the Starks and the Lannisters. Daenerys consistently gains momentum in this category as her influence in Essos grows, and as additional denizens of Westros seek her out. Interestingly, Theon and Stannis do nearly as well in betweenness. As for Stannis, with his longstanding claim to the Iron Throne, and his connections to Jon Snow, he forges a triangle between communities Baratheon, Lannister and Stark. In summary, Tyrion wins the three most straight-forward categories, while Jon wins the two subtler measures.

In the same series

PageRank is the best measure for narrative dominance: important things happen when influential people interact. In my opinion, Jon deserves a bonus for winning this category.

Degree Centrality

Finally, betweenness centrality shows how important a character is for unifying the story as a whole. Again, Jon wins this important measure. Meanwhile, Tyrion trounces Jon in eigenvector centrality, meaning that he is connected to far more influential people. It is a tough call! However, there are more volumes to come, and Jon clearly has the momentum. Here is the progression of PageRank values by volume:. Stannis has the largest net increase in PageRank, yet he does not have the narrative momentum.

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Depending on how Daenerys wields her might and influence and dragons when she arrives in Westeros, she could take second place, or even the top spot. Unless Tyrion finds himself on the Iron Throne, he seems destined to lose the network centrality game to Jon and Daenerys. Finally, it is clear that Stannis deserves the next spot, especially since he is not a point-of-view character.

So here is the ranking, as I see it, after the first five books. As for honorable mentions, Arya performs incredibly well when the books are taken as a whole, though her performance from book to book has been uneven. Clearly, her journey has been an enduring adventure, so she seems poised to return to the main narrative with great effect.

Theon performs exceptionally well in PageRank, especially compared to the number of his connections and interactions. Meanwhile, Sansa underperforms in this category, finishing behind the departed Ned, Catelyn and Robb, in spite of her high degree and weighted degree.

So it seems that the momentum is not with the Key to the North at this point in the narrative. Search for:. Communities Ordered by size, here are the 10 main communities. Degree Centrality First, we consider degree centrality, which counts the number of distinct connections to other characters.

A Song of Math and Westeros

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