Small World Networks Theoretical Framework for the ResULTS Project

A small world network’s resilience comes from a combination of its cluster which encourages cohesion and the interconnections between the clusters which encourages flows of information and ideas. Is there a small world network among Orkney’s livestock farmers? We do not know yet.

A number of years ago, I was in Rome during a European holiday. I was having dinner in a restaurant down the street from FAO headquarters and next to the pyramid. It was one of those restaurants where you sat at the counter and selected from the food displayed behind it. Next to me was a man reading a book in English. When I asked where he was from, he said he was American. Since I was also American, I asked where he was from and he told me he was from the Washington, DC area. Since I was living in the DC area at the time, I enquired which part of the DC region he lived. He said Virginia. This was beginning to get spooky because I also lived in Virginia. When I asked which part of Virginia, he said Alexandria. Yep, you guessed it, I also lived in Alexandria. When I asked where in Alexandria, I was told just off of King Street. And yes, I lived just off of King Street. It turns out we lived one mile apart from each other and had visited the same Greek restaurant in the shopping centre between us. When things like this happen we often remark what a small world this is!

There was curiosity about why experiences like mine seem to happen regularly. What network mechanism drove this? Related to this was a debate in the 60’s about how many network steps it would take to connect any two people in the United States. Some guessed as many as 100. In the 1960’s, Stanley Milgram conducted an experiment to answer this question.

He asked 160 random people in Wichita, Kansas and Omaha, Nebraska to forward a folder to two people living in Boston and Sharon, Massachusetts. The key was not to mail it directly to them but to use the sender’s own contacts who may know the targets or people who knew these targets to forward the folder. When the researchers calculated the average number of network steps that 42 folders that made it to Massachusetts, it turned out to be around six. This is where the concept of six degrees of separation comes from.

The 1991 play of John Guare, Six Degrees of Separation, gave the impression that everyone on Earth is no more than six network steps away from anyone else. However, there are two caveats to this. First, six was the average number of network steps in Milgram’s experiment. This means that it can less than six network steps or more than six. Second, there are a number of isolated groups that are not connected to any society. This is becoming rarer but these still exist.

If you want to have some fun with six degrees of separation and small world networks, check out the Oracle of Bacon which does the six degrees of separation of Kevin Bacon the movie actor.

Others have replicated Milgram’s average number of network steps to connect two people. Duncan Watts did this with 98,000 email users. Watts along with Steven Strogatz came up with a model to explain small world networks. Small world networks have two features, a high clustering coefficient and connectivity between the clusters. A high clustering coefficient means the networks has the strong tendency to consist of groups of people who are highly interconnected with each. Each of these clusters are connected to at least one other cluster. The figure below gives one example of a small world network.


You can see in the above network that it will take a maximum of seven network steps to get from one node to any other node. In this network, the clusters are connected to their immediate neighbours. However, there is no requirement for this configuration. Clusters can also be connected to clusters across from them.

So, what does this type of network have to do with resilience? Small world networks tend towards resilience as the clusters tend to remain stable over time and removing a few links will still allow any node to connect any other. If only one link connecting clusters is removed in the above network, you will still be able to get to all nodes but it may take many more network steps. If enough links are removed, the ability to get to every node disappears. The way to prevent that is by having more interconnecting edges between clusters.

Imagine each cluster is a separate island in Orkney and the connecting link between each island is representing a personal relationship between two persons on each island. This is fine as it stands but it is important to state that social networks carry the negative as well as the positive. What happens if the two people connecting the islands disagree on something major, such as Brexit or Scottish independence?

That is why it is important to have redundant interconnecting ties between the clusters to keep this small world network resilient. In the case of Orkney, it could be ties based on school attendance, breeding societies, association membership, etc.

While the Watts-Strogatz small world network model explains what happens in the Milgram experiment, you should realise that there is no perfect small world network in the real world. The real world is messier. But, it does explain why a small world network can be resilient.

So, a small world network’s resilience comes from a combination of its cluster which encourages cohesion and the interconnections between the clusters which encourages flows of information and ideas. Is there a small world network among Orkney’s livestock farmers? We do not know yet. If there isn’t one, would it be possible to do a network intervention to help establish one among Orkney livestock farmers? We do not know yet. Hopefully, our research will help us find out.

Post comment

Your email address will not be published. Required fields are marked *

© 2018. ResULTS