Our “A Clash of Kings” network for consists of 259 nodes (characters) and 775 weighted edges, accounting for 6,360 interactions. Character names are sized by PageRank centrality. Character nodes are sized by betweenness centrality. Edge thickness corresponds to edge weight.
There are six prominent communities for this network. Clockwise from the top, they are:
- the far North (Jon),
- the Night’s Watch recruits and Lannister bannerman (Arya),
- the Stark/Baratheon alliance (Stannis, Robb, Catelyn, Renly),
- the Red Waste of Essos (Daenerys),
- King’s Landing (Tyrion, Joffrey, Cersei),
- the Iron Islands and Winterfell (Theon and Bran).
Except for Daenarys in the Red Waste, the dynamics within these communities are rather complex.
- Jon Snow’s community splits neatly into two separate groups: the Night’s Watch and the freefolk beyond the wall.
- Arya also brings together two distinct groups: Yoren’s recruits (heading from King’s Landing to the Night’s Watch), and Tywin Lannister’s allies, including Gregor Clegane and Armory Lorch.
- Theon and Bran anchor a split community of the Ironborn and Winterfell, with the community joined, yet cleaved by Theon’s betrayal.
- King’s Landing centers on the ruling triad of Tyrion, Cersei and Joffrey.
- The final community combines the Baratheons and the Starks, as they react to the treachery of the Lannisters. In particular, both Robert and Ned are part of this community (and not part of King’s Landing) as their surviving Houses grapple with their demise.
Looking broadly across all of the centrality measures, Tyrion has taken up the mantle that Ned Stark held in “A Game of Thrones.” Acting as Hand to an ill-equipped King, Tyrion becomes one of the most powerful men in Westros. Joffrey scores well because everyone is talking about him (but mostly negatively) in both King’s Landing and in greater Westros. Likewise, Arya’s scores are inflated because many are concerned about her whereabouts. Cersei and Stannis both earn their consistently high marks, though neither approaches Tyrion’s scores.
Degree Centrality and Weighted Degree Centrality
Let’s look at the centralities in more detail, starting with the simplest measures. The top characters in degree centrality (number of connections) are
- Tyrion, Joffrey, Cersei, Arya, Stannis, Robb and Catelyn.
With respect to weighted degree centrality (number of interactions), the list is fairly stable:
- Tyrion, Joffrey, Cersei, Bran, Stannis, Arya, Jon.
The new additions (Bran and Jon) are point of view characters who interact with relatively fewer people, but are crucial to the broader story.
PageRank’s feedback loop captures more narrative tension than the simple interaction measures above. The top characters are
- Tyrion, Theon, Arya and Joffrey.
Theon’s impressive showing is worth a closer look, especially in comparision to Daenerys (who ranks 12th). Like Daenerys, he has very few connections outside of his community: the ironborn prince only connects to Catelyn, Robb and Eddard. Unlike Daenerys, these are strong connections, so they contribute significantly to Theon’s PageRank. Theon further benefits from Bran’s importance, which itself is bolstered by the other Stark children. In short, Theon’s siege on Winterfell is highly rewarded by PageRank since it garners the attention of many important characters. Meanwhile, Daenerys is all but forgotten on Westros due to the War of the Five Kings. Her only connections beyond Essos are to the Usurper, Robert Baratheon, and Barristan Selmy, whom she encounters in Qarth under his alias, Artsan Whitebeard.
Eigenvector centrality gives a different ranking:
- Joffrey, Cersei and Tyrion
score the highest. Following a gap, we have
- Robb, Stannis, Sansa and Arya.
This measure captures how many powerful connections you have, ignoring your actual influence over that connection. Stannis and the three Stark children have potential to develop their importance if they can garner more attention from their connections.
Betweenness centrality tells a distinctive story. Arya and Jon come out on top, followed more distantly by Theon, Tyrion, Robert and Robb. Arya, Jon and Theon are crucial in tying the narrative together as a whole. Meanwhile Daenerys’s roaming band in the Red Waste is not large enough to boost her importance to the same degree.
And the Winner is…
Tyrion, for sure! The Imp is the leader in three categories (degree, weighted degree, and the all-important PageRank). He loses out to Joffrey and Cersei in eigenvector centrality (but hey, it’s hard to beat the King). Meanwhile, his betweenness score is the highest among the non-Starks, who themselves are in a bit of disarray in this volume.
Second place goes to King Joffrey. While he may not be a powerful ruler, he is clearly on everyone’s mind, across the Seven Kingdoms. His only demerit is for betweenness, but he is safely ensconced in King’s Landing, protected by his small council. So, of course he is a bit isolated.
Arya deserves third place, for her impressive PageRank and betweenness scores, backed by her solid performance in the other categories. She travels the widest narrative arc, and is rewarded. Fourth place is a tight race between Robb Stark and Stannis Barratheon. I give Stannis the edge, for his consistency. So our ranking is:
Clearly, Theon deserves a very special mention for his second place PageRank performance. His return to the Iron Islands, and his bold betrayal of Winterfell add a new dimension to the narrative. Similarly, Jon gets a nod for his second place betweenness score, though his journey has taken him far from the action for now.
Finally, Daenerys is quite marginalized and impotent in this novel, and her centrality scores reflect this. She has lost Drogo, her son, and finds herself at a new low. But she is also now the mother of dragons. She has started to forge a new path, and is slowly finding her way.