# The topology of Shakespearean Social Networks

## Tags: projects, programming, research

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In a previous article, I have already talked about the motivation behind analysing social networks of Shakespeare’s plays. Since then, I have pursued this subject somewhat further. In particular, I took some time to formulate a more methodical analysis approach.

The result is a nice short paper, titled *‘Shall I compare thee to a
network?’—Visualizing the Topological Structure of Shakespeare’s
Plays*. I was very honoured to present this at the 2016 Workshop on
Visualization for the Digital Humanities at IEEE Vis 2016. It was a great venue
with lots of interesting papers and I urge you to take a look at the list of
submissions.

Our paper follows the basic strategy outlined in the previous blog post. Hence, we first extract a co-occurrence network between characters of a play is being extracted. There are numerous ways of doing that, and each different way influences the structures that may be detected in a subsequent analysis step. In the paper, I present two different weight schemes. One is based on the amount of speech uttered by each character, the other one measures the point in time at which characters start to interact with each other.

The co-occurrence network is then subjected to a topological analysis based on persistent homology.
Basically, we consider the network to *grow* in accordance to the weights. This permits us to treat
it as a *graph-based filtration*, which in turn means that we may calculate *persistence diagrams*
and, from that, derive a measure of dissimilarity. The interesting thing here is that this approach
results in well-defined distances between individual plays—meaning that we can measure
structural differences and structural similarities.

The paper contains some results that appear to indicate the utility of this approach. Without
further training, our algorithm is capable of figuring out that *All’s Well That Ends Well* is
a comedy that is structurally extremely dissimilar to all remaining comedies. This is interesting,
insofar as this play is considered to be one of “Shakespeare’s problem plays”.

In the paper, we describe more results of the same ilk. I have made the networks available on GitHub, where I also plan on uploading code for calculating the dissimilarity measure.