To answer this question, I am gonna look at a dataset of shared plotlines throughout the whole show. That is, which subset of the six characters appeared together in in a plot during an episode. These plots can range from simply hanging out together in Central Perk to some hanky-panky in the bedroom. We can see a shared plotline as some form of interaction and therefore analyse the show from a

Clicking through these figures, I always start thinking about all the funny scenes of the respective seasons. I think it is time to rewatch it for the 10th time!

A simple network is usually represented in an adjacency matrix $A$ where $A_{ij}=1$ if there is a link between actor $i$ and actor $j$ and $A_{ij}=0$ otherwise. Since in our case, edges have no

$$ Av=\lambda v$$

The entries of the vector $v$ are then used to rank the actors of the network. But how can we interpret $v$? The short and simple (and slightly wrong) explanation is, that actors are considered important, if they are connected to other important actors. So it is not just the number of connections, but also the

When we deal with hypergraphs, we are faced with the problem, that we can no longer represent our network with an adjacency matrix since links can have more than two endpoints. Instead, I will use the so called

In order to use the eigenvector centrality concept on $E$, it first has to be projected to a square matrix in the

$$E^TEv=\lambda v.$$

Original size can be found here |

Now lets consider all interactions of all episodes at once. That is, we want to know who is the most central character in the show. And it is...

Of course one could question my relatively simple approach on finding the central characters and of course one could question the dataset. But then again, this is a blog about mildly scientific topics, so...yeah... take the results as they are but do not over interpret them. Also, because i am going to show in an upcoming post, why the results are as they are.

A big thank you goes to Alex Albright who not only provided the dataset but also some valuable discussions which actually motivated me to write this blog entry. Please check out her blog too!

Labels: Network Analysis, TV Show