Using Heads and Tails to Make Heads or Tails of Caltech Houses

I have previously introduced and discussed my BioFabric version of the Caltech Houses (i.e. dorms) network that I based on the data from Traud et. al. 2011, and I am going to talk about it a little further here. If you want to view the whole network, and you don't mind the 3.8 MB download, take a look at the scrollable version.

In this post I will discuss the structure of the network within one of the dorms. Again, as with previous posts, I'm just going to describe what features I am seeing by eyeballing the BioFabric visualization. I'm not going to back up these claims by using network tools to analyze the structure; I'll leave that an an exercise to the reader. My goal here is to help you to build up your visual "network fabric intuition".

Recall that this Caltech dorm network was drawn by grouping the students using the provided information about which dorm each student lives in. So there are eight horizontal bands in the fabric that correspond to these eight dorms. Each dorm was separately laid out using the default BioFabric layout algorithm on just the intra-dorm links before they were combined into the full network. This means that the head (left end) of each dorm starts with the most popular student in that dorm (considering the dorm in isolation), followed immediately by that most popular student's Facebook friends. Meanwhile, the tail (right end) of the dorm is typically going to tend to show students with fewer friends in the dorm and/or more indirect connections to the most popular student. Keep in mind that this tendency towards low-degree students in the tail is broken by those students in the tail who do have many in-dorm friends, but who are several degrees of separation away from the "in crowd" at the head. That's the consequence of the breadth-first search used by the default layout.

Note, by the way, that the presentation I am using here is different from the one considered in the original paper, which showed how well the dorm assignment corresponded to the clustering they detected in the Caltech network via clustering algorithms. Instead, my approach here is to look at what we may be able to observe about the network given that it has been explicitly grouped using those dorm assignments; this presentation provides no insights into larger social groupings that cross dorm boundaries. 

Below are two figures showing portions of Dorm 4, which appears to be a pretty typical example of the dorms. Though you can pick out each dorm easily enough as you scan the network just by following the shape of the diagonal, I have added the red horizontal lines in these figures to clearly show the extent of Dorm 4 in these extracted segments. The first figure shows the head end, i.e. the popular students:

Click on picture to enlarge

So, the first thing to notice is that 623, on the far left (and the most popular student in the dorm), is pretty well connected within the dorm. His/her in-dorm edge wedge covers about 75% of the students in the dorm. (Remember, due to link grouping, the in-dorm edge wedge appears to the left of the out-of-dorm edge wedge for each student. Furthermore, the out-of dorm wedge appears as two wedges here, since it is split into above-node and below-node pieces.) Then, 623's most popular friends do a pretty good job of matching 623's friends in the dorm, since we can see that their in-dorm wedges very roughly approximate 623's. Those friends also do a good job of bringing in some more students, such that by the time we get to the ninth student on the right side of the head, at appears that well over 80% of the students in the dorm have been linked to.

It's also interesting to note that 623, while the most popular student in the dorm, has a majority (maybe greater than 67%?) of his/her friends outside the dorm. It appears that 633, the next in line, is almost as popular as 623 in-dorm, but is also much more inwardly focused on Dorm 4! 

Now look at the tail end of Dorm 4, again with the red lines to show the extent of the dorm:

Click on picture to enlarge

Note first that this short tail stretch actually shows the links for just over 50% of the students in the dorm (241, on the left, is not quite below the half-way point between the red lines). We can also see here what is going on with the 10% or so of the students who are not directly connected to the popular core; they start around the prominently labeled student 734 near the far right. Even at this scale, you can spot sort of a "phase change" in the edge wedge pattern as we get to just to the left of 734: the in-dorm edge wedges stop connecting to the popular students at the top of the Dorm 4 band. I'll discuss this group a little more below.

But turning back to the "typical" tail-end students in Dorm 4, we see that they are all connected to that central core at the head of the dorm, since they have links going to the top of the dorm band. Perhaps not surprisingly, most of the tail students are connected to social groups centered on the top core 50%, but not so much amongst each other. We can see that because the in-dorm edge wedges here typically show few edges below the diagonal (226 and 606 are notable exceptions). Another feature worth noting is that even these students with relatively few in-dorm connections almost all have at least a few out-of-dorm connections as well.

Finally, the isolated tail group starting around 734 is shown below in detail as an extracted submodel, again with red lines to indicate the bounds of Dorm 4. Note how 734, 722, 728, 738, and (to a lesser extent) 744 form a somewhat cohesive social unit, with many common social connections focused outside of the dorm:

Click on picture to enlarge

So that's my attempt to make "heads or tails" of one of the dorms in the network just by visual inspection of the fabric. I expect one more posting on this network: stay tuned!