International borders are strange places. A U.S. citizen crossing the border to Mexico can stay for 72 hours and requires a visa for any longer. But Mexican citizens traveling the other way require much-prized visas to make the journey. The U.S.-Mexican border is consequently asymmetric and often tense.

The U.S. border with Canada is a very different affair, with citizens from both countries able to travel back and forth with ease and without visas.

In both cases, the border reflects the nature of international relations between the countries. Visa-free travel is the result of the friendly link between the U.S. and Canada. And the more stringent visa requirements operating at the U.S.-Mexico border is a clear indication that this relationship is more troubled.

And that raises an interesting question. If visa-free travel is a proxy for good international relations, then what does it reveal about the geopolitical architecture of the planet?

Today, we get an answer thanks to the work of Meghdad Saeedian at the Shahid Beheshti University in Tehran, Iran, and a few pals, who have studied the network of links between nations that allow visa-free travel for each other’s citizens.

These guys say the resulting network divides the planet into four clearly delineated communities plus an additional single outlier that doesn’t fit into any community. And since these communities are the result of a complex geopolitical history, this form of mapping provides important insights into the nature of international relations.

Saeedian and co begin by creating a network based on the visa policy of all 222 of the world’s nations. In this network, a link exists between two countries if they both allow visa-free travel for their citizens. For example, in this network, there is a link between the U.S. and Canada but not between the U.S. and Mexico.

This leads to a network of 222 nodes with over 5,000 two-way visa-free links. (Incidentally, there are over 10,000 one-way links in the visa-free network that Saeedian and co do not count.)

This allows them to use the standard tools of network science to analyze the nature of this web. For a start, they look at the in-degree distribution, which reveals the number of countries that allow visa-free travel from other countries.

A small number of countries have few inward links, meaning that the citizens of almost all countries require a visa to get in. These are countries such as China, North Korea, Sudan, and Iran.

Then there are countries that have a very high number of inward links; these tend to be countries with strong tourism industries.

Finally there is a peak of countries in the middle with similar numbers of inward links. These are mainly European countries which share a common border arrangement known as the Shengen agreement and so have similar numbers of inward links.

An important question is how this network is divided into clusters. In other words, what countries share similar border arrangements with each other? Saeedian and co answer this using standard algorithms for finding clusters in networks.

And the results are clear. “Based on the visa status of all countries, community detection reveals the existence of 4 + 1 main communities,” they say.

It’s no surprise that Europe comes out as one of the densest clusters, given that visa-free is possible throughout most of this region. This cluster extends throughout the developed world, including, Japan, Australasia, North America, and most of South America.

Another tightly knit cluster consists of countries mainly from Asia and southwest Africa such as India, Malaysia, North Korea (but not South Korea), South Africa, and, curiously, various Caribbean islands. There is also a cluster of countries in eastern and northern Africa.

The least tightly knit group consists of Russia, certain Eastern European countries, and nations that gained independence from the former Soviet Union. This includes Uzbekistan, Kyrgyzstan, and other “Stans,” Serbia, Macedonia, and other Balkan states as well as a variety of Middle Eastern countries such as Saudi Arabia, Kuwait, and Bahrain. Interestingly, this diverse group is connected via Turkey, perhaps reflecting this country's complex history.

Saeedian and co do not comment on the geopolitical implications of the fact that this group is less tightly knit than the others, but it may have to do with the rapid changes in the nature of these nations and their international relations in the last 30 years or so.

A single outlier in all this is China, which does not allow visa-free travel for its citizens. Saeedian and co put it in a category of its own to reflect its increased status in the world.

That’s an interesting study that provides a relatively simple way to characterize and visualize the geopolitical landscape of the planet. An interesting future task would be to see how this network has changed in the past. If these changes are any guide to the future, then Saeedian and co could have a powerful tool on their hands.

Ref: http://arxiv.org/abs/1601.06314: How Visas Shape and Make Visible the Geopolitical Architecture of the Planet