Regions and embassies as a social network.
Written by Starrie Backstrom and Kleinberg introduce a method for finding romantic partnerships on a social network like facebook. The question is, what happens when we apply this to the embassies in nationstates?
Here's a picture of the embassies connecting all the regions. (warning: large image). The vertexes and label names have been removed but the general layout is still visible. At this zoom, there's a visible cluster near the bottom left -- those are the regions for the fifty states in USA, many of which have interconnected embassies. Although most of the mass is clustered into a shapeless blob, there are some bright outliers -- regions with many embassies, and, looking farther out, small clusters of regions which are not connected at all to the rest of the regions.
Clearly, we need to zoom in to identify smaller structures. Here are three smaller graphs. The "centers" are F R S S N, Strategos Prime, and Srbija respectively, and each graph contains every region which has an embassy with the center. The neighbors of the center are also connected to each other with embassies, but how can be determine the romantic partner?
F R S S N
Strategos Prime
Srbija
Backstrom and Kleinberg's method measures the "dispersion" of each potential partner:
First, remove both the center region and the partner region.
Then, count how many of the neighboring regions, which were previously connected, are now disconnected from each other.
There are some subtleties, but this will do for now.
This algorithm works because romantic partners often bridge the two communities of friends together. While a close friend might be well integrated into one's social network, removing the friend has little effect because the community is already interconnected. This is less the case with romantic partnerships.
It turns out that the partner of F R S S N is The International Communist Union. This may not be obvious at first, it might look like The Illuminati is closer. However, since the regions the Illuminati has embassies with are already closely connected, the removal of the Illuminati does not have any significant effect. On the other hand, The International Communist Union unites more seperated regions together.
Try to see if you can figure out what the romantic partner of Strategos Prime and Srbija is.
Spoiler: click to toggle
This is purely observational, but the social network graphs on facebook have much more distinct features than the graphs of embassies in nationstates. Perhaps this is due to the fact that they are used differently. In anycase, it makes picking out the partners much more difficult.So now that we've identified the romantic partnerships of individual nations, we'll take a look at all the partnerships of regions, in other words, the "network of love". Although "ideally", we should find pairs representing relationships and single vertexes representing single regions, we can tweak the criteria for a relationship downwards slightly to get some interesting results.
It seems that a large number of regions have relationships centered on a single region, like The Illuminati and Iura Pecunia et libertas. Polygamy on a vast scale.
I want to make it clear that these graphs are not of a region and it's neighbors, they are of regions which are all romantically connected to each other.
The explanation is simple. Just by having hundreds of times more embassies than most others, a region like The Illuminati becomes the partner of a vast number of regions. In a network like facebook, this effect is much less pronounced. We can correct for this by dividing the dispersion by the number of embassies a region has to find it's adjusted dispesion and get some different networks.
These networks are better spread out. However, there is still a bias towards larger regions because they show up in more region's neighborhoods. If we divide again by the number of embassies, we get even smaller and more linear looking networks.
Curiously, not one of the relationship networks we've seen has any sort of love triangle. After a lot of searching, I managed to find just one.
Communist romance, anyone?
