- If you are new to Network Science, be sure to read A Primer on Network Analysis before continuing.
- Spoiler Warning: the text below does make reference to events in various seasons. But looking at the diagrams will tell you a bit about who is “important” without revealing details.
- Also, you might also want to start with The Novels— I wrote those pages first.
The network for Season 1 has 127 nodes (characters) and 550 weighted edges, accounting for 6,525 interactions. The nodes are colored by community. The labels are sized by PageRank centrality. The node’s size corresponds to its betweenness centrality. An edge’s thickness indicates its weight.
The network divides into five main communities. They are (clockwise from the top):
- the Night’s Watch (Jon Snow, Sam, Pyp)
- the Lannisters (Tyrion)
- the Dothraki (Daenerys, Drogo, Jorah)
- King’s Landing (Ned, Robert, Arya)
- the Starks (Catelyn, Robb)
In addition, there are two small communities: the doomed Night’s Watchmen from the prologue; and the pair of orphans, Lommy and Hot Pie.
Perhaps the most distinctive feature of this network is how tightly concentrated the action is. There are strong triads in each community. For example, the following triangles catch your eye:
- Ned, Robert, Cersei
- Ned, Peter, Varys
- Ned, Arya, Sansa
- Sansa, Joffrey, Cersei
- Catelyn, Robb, Bran
- Jon, Sam, Pyp
- Daenerys, Drogo, Viserys
- Daenerys, Jorah, Viserys
Tyrion’s community is looser, capturing his independent spirit. He does anchor two subtler triangles: with Tywin and Jaime, and with Bronn and Shae. The former triangle captures his ties to House Lannister, the seat of his power and station. The latter is the motley pair of allies that he develops during his misfortunes.
As with the first book, there are many strong ties between communities. We can see the strain on the Stark family: their familial ties are being stretched and tested. We also see the conflict between House Stark and House Lannister, most prominently with the many connections from lions Tyrion and Jaime to the direwolves of Winterfell.
Of course, we expect this network to be simpler than the network for the book Volume 1: A Game of Thrones. We can see how the writers have pared down the narrative, and made it more focussed. For example, Jamie is a much stronger presence in the TV show. Along with Ned, Catelyn and Tyrion, the Kingslayer binds the Stark, Lannister and King’s Landing communities together. Likewise, each triangle explicitly captures a distinct plotline. In the book, George R. R. Martin had the luxury of allowing the reader connect the dots a bit more through indirect relationships.
On the other hand, sometimes the absence of ties is just as telling as their presence. For example, notice the relatively weak ties between the following pairs: Drogo and Jorah, Arya and Joffrey, Sansa and Jon, Catelyn and Jon. These missing edges frustrate some natural triangles, creating tension in the network and narrative, alike.
Finally, this network has one fewer community that the book: the royal children remain part of the larger King’s Landing community. In addition, Catelyn remains in the Stark community, rather than in a Riverlands community with Tyrion. It seems that the familial ties are more explicit in the series.
Narratively, Season 1 is straight-forward (especially compared to the complexity to come). The shocking season’s end reveals that the show isn’t what you expected it to be. Rather than achieving a tidy resolution, hindsight reveals that the whole season has been a set-up for a much more complicated, sprawling, and dare I say unhappy narrative. But since the majority of the season plays out directly, we expect to find straight-forward dynamics in the network as well.
And we are not disappointed. The rankings across the various centrality measures are relatively stable among the top characters. As a quick reminder, here is the intuitive way to think about these five measures:
- Degree centrality: how many people you know
- Weighted degree centrality: how many interactions you have
- Eigenvector centrality: how many important people you know
- PageRank: how many important interactions you have
- Betweenness: do you help to connect the network together?
With a single exception, the top four characters across all categories are
- Ned, Tyrion, Catelyn and Robert.
At this point, the centrality measures reassure us that this is the story of House Stark, doing their best to serve the realm. Tyrion, the misfit philospopher, humanizes the arrogant Lannisters. Perhaps is role is to pick up the shattered pieces of House Lannister once their scheming is revealed?
Cersei slips into fourth place for eigenvector centrality. I find “over-performances” like this particularly interesting. (Typically, I start by using degree and weighted degree as my benchmarks. Then see how the other three metrics overperform or underperform.) So Cersei is an “important” character that gets less screen time. She seems to be the mastermind of the machinations against Robert. Perhaps we are given less exposure to her ways in order to heighten the intrigue.
Let’s look at the second tier of characters, across the five measures
- Degree centrality: Robb, Cersei, Arya, Jon, Sansa, Petyr (Littlefinger)
- Weighted degree centrality: Daenerys, Jon, Cersei, Robb, Sansa, Petyr
- Eigenvector centrality: Joffrey, Robb, Arya, Petyr, Sansa
- PageRank centrality: Robb, Arya, Jon, Cersei, Joffrey, Petyr
- Betweenness centrality: Daenerys, Jon, Robb, Arya, Pyp, Jorah
We see a lot of stability here, with Jon, Robb, Arya and Petyr consistently appearing in most categories. These measures clearly identify Littlefinger as a man to watch (more so than his rival schemer Varys).
Perhaps the most unusual measure is betweenness centrality, where Pyp and Jorah sneak into the top 10. This category rewards narrative glue: Pyp seems to be the stand-in for the Night’s Watch recruits, while the khaleesi’s advisor, Jorah (or is he informant?) tenuously connects Daenerys’s journey back to the main action. Daenerys and Jon do well in this connecting measure, as well as in weighted degree centrality. They may not know many people, but they do get a lot of screen time.
Eigenvector centrality highlights a subtler dynamic. We already mentioned that Cersei cracks into the top tier here. Joffrey, heir to the throne, joins her in the second tier. This reminds us that the main tension focuses on the Iron Throne, in spite of our personal investment in House Stark. Meanwhile Jon (13th) and Daenerys (34th) are nowhere to be seen.
And the Winner is…
As we know, Ned is the true protagonist of Season 1, and he leads all five measures. Interestingly, Robert does not perform as well in the TV series as he does in the book. This is due to the streamlining of the adaptation. Yes, Robert is central to the plot (as his second place eigenvector centrality attests). However, for the most part, the intrigue unfolds around him, while he remains drunk and distracted.
Tyrion takes second in four out of five categories. He underperforms in eigenvector centrality because he is not directly involved in the ruling and the scheming in King’s Landing. But he provides narrative balance to Ned (and the Starks), more than any other character. Catelyn, a strong and capable woman of action, takes third in every category. Robert takes fourth place in four categories to complement his second place eigenvector centrality.
After that, it is less clear who to award fifth place. Robb, Arya and Jon split the measures. Robb and Arya benefit from their attention from Ned and Catelyn. Jon has more interactions, and helps to connect the network. There is not clear answer here, though it is clear from the plot constructs that Jon has an interesting journey ahead. However, that speculation is not enough to overcome his other weaknesses. So I will stick to the straight PageRank ordering for this season.