In the last article in our Survivor Alliance Analysis, we were able to build alliance networks out of voting data. This opens up the tools of data science and network analysis.
In this article, we calculate some standard metrics of the alliance networks, namely the centrality metrics degree, closeness and betweenness and the clustering metric. This will hopefully enable us to compare and contrast the different seasons of Survivor.
This is the third article in my Survivor Alliance Analysis series. The other articles in the series are:
- Scraping the Survivor Wiki with Beautiful Soup
- Computational Analysis of Survivor Alliances
- Survivor Alliance Networks Visualized
- Network Analysis of Survivor Alliances
There are two ways we can approach network analysis. First, we can perform an intranetwork analysis, comparing nodes belonging to the same network. Second, we can perform an internetwork analysis, comparing two or more different networks with one another. Our approach in this article is the second one, as our goal is to compare and contrast the different seasons of Survivor.
We will use four metrics to perform network analysis: degree, closeness, betweenness, and clustering. The first three metrics are all considered as centrality metrics, since they measure how important nodes are in the network. These metrics are used, for example, to determine the most influential person in a social network. The fourth metric, clustering, is a measure of the density of ties around a node, i.e. how likely your friends are friends of each other.
I give a brief rundown on these four metrics in Network Metrics Explained.
Comparing Different Seasons of Survivor
We calculate the metrics in two different ways. First, we will look at the average value of the metric over the whole network. In other words, we average the metric over all castaways in the alliance network. Second, we look at the maximum of the metric over all nodes or castaways.
Note: Our calculations for the centrality metrics are alliance-index-weighted, while the clustering metric is not.
The Amazon, Samoa and Cambodia have the top three largest average degree, while Borneo has the smallest one. A castaway with a high degree is someone who has voted with a lot of other castaways, so that means that a season with high average degree is one whose castaways have worked with almost everyone, regardless of alliance lines.
In terms of average closeness, Worlds Apart has the largest one and Thailand, Palau and RI have the smallest. Intuitively, closeness can be thought of as how tight the alliance network is. A season with large average closeness is one wherein the castaways are all ‘close’ to one another.
For betweenness, Borneo reigns supreme and, again, Thailand, Palau and RI lag behind. A node with high betweenness is one which acts as a bottleneck between disconnected clusters. That is, to go from one location in the network to another, the path must go through the node. So in this case we see that the three with the lowest ones coincide with the networks with disconnected clusters since no node acts as a bottleneck.
Some seasons have large average clustering coefficient, while some have a small one. The ones with the large clustering coefficient coincide with those with disconnected clusters that are almost complete or fully connected – Thailand, Palau and Redemption Island. The ones with small clustering are those which are more homogeneously spread out like Gabon and Nicaragua. Clustering basically measures the formation of cliques. In this case, we can think of seasons with high clustering as having tight alliances and those with small clustering as having fluid ones.
A season with large maximum degree is one which has a castaway that was almost everyone at one point or another in the season. In this case, Africa and Philippines are on top.
For maximum closeness, we see that Worlds Apart, again, is on top and Thailand and RI are on the bottom. In the case of maximum betweenness, All Stars, South Pacific and One World rank highest, since in each of those there is/are a bottleneck castaway/s (Shii-Ann, Cochran, Tarzan/Troyzan) which connects all others.
Every season has a castaway with perfect clustering, except for Kaoh Rong (well, it’s not really significant, since it’s still at 0.95). This means that there’s someone in every season whose neighbors in the alliance network are all connected as well, which is basically what an alliance is.
So, that was fun. That concludes the Survivor Alliance Analysis. A possible future project is to visualize the time-dynamics of the alliance network… but at the moment let’s move on to some other TV show or movie.
If you’ve got some thoughts on the alliance networks and the network metrics we calculated, I would love to hear all about it below.