Scale Free Networks Theoretical Framework for the ResULTS Project

In 1775, at the start of the American Revolution, the British were determined to disarm the rebel militias and seize their military supplies.

In 1775, at the start of the American Revolution, the British were determined to disarm the rebel militias and seize their military supplies. When the rebels in Boston, Massachusetts got wind of this, they sent two riders to warn the militias in the outlying towns that the British were coming. Setting out on different routes, Paul Revere and William Dawes rode to warn the militias and the towns from Boston to Lexington and Concord. The warnings allowed the militias to be ready. However, the two rides had very different results. William Dawes’ ride did not cause a general rising of the militias in the areas he travelled through. On the other hand, the Revere ride did instigate a general rising which meant the local militias were ready when the British troops arrived in Lexington and Concord.

Why was Revere’s ride much more successful than that of Dawes? Malcolm Gladwell in his book, The Tipping Point, argues that this is because Revere is what he calls a connector. Gladwell defines a connector as someone who knows a lot of people. Gladwell had a test where he would ask people to count how many family names they recognised from 250 names chosen from the Manhattan telephone directory. One connector named Roger Horchow, a Broadway producer and investor in shows like Les Miserables and Phantom of the Opera recognised around 100.

Paul Revere was similar to Roger Horchow. Revere knew a lot of people on his route and knew who to go to spread the message. Connectors like Revere play a very important role in networks. One of those roles is shortening the distance between people in the network helping to lower the degrees of separation between two people discussed in the last blog.

In social network analysis, a network that has connectors in it is known as a scale-free or power law network. Why power law? Imagine that the number of connections people have in the network is based on the power of 2. Therefore, they would have the following number of connections in the network: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024. Most people in the network will have 1, 2, 4 or 8 connections. However, connectors such as Paul Revere and Roger Horchow would have 512 and 1024 connections in the network. It should be mentioned that true power law networks exist in real life.

It is this feature that introduces resilience into scale-free networks. US airlines organised the flight network around hubs. The hub would be at a large airport in a large city where flights to all over the USA would fly from. The thinking is that their rivals knock out route from this hub through competition but they would be unable to knock out every route from this hub. Connectors act like hubs in their networks. They add resilience to the network.

Research has shown that there are two ways break apart a scale-free network. First, is by directly attacking the hubs. An example of this is the denial of service attacks on key Internet hubs that cause large scale disruption. Second, would be a cascading failure. This is where one part of the network fails but this failure causes a connecting part of the network to fail which causes those parts linked to this part of the network to fail and so on. An example of this would be the huge power blackout in the western United States in 1996. During a heatwave in the state of Oregon, a major power line expanded and sagged into a tree. The resulting flash caused the line to go dead. The rerouted power went through lines that couldn’t handle the surge and these also failed. This started a cascading failure that ended up with no power for the western United States.

So, what does this have to do with livestock farming? The network of animal movements is now a scale-free network. Why? Take a look at this network diagram from a study of animal movements in Denmark.


The most notable feature in the network diagram is the star in the centre. This represents the market where animals are bought and sold. Almost all the links in this network go to and from the market. Unless the market gets eliminated, this network will continue. For Orkney livestock farmers, they too find themselves in a scale-free animal movement network. The primary hub will be the Orkney Auction Mart and the secondary hub will be the Thainstone Mart outside of Aberdeen. It is difficult to see a direct attack on these hubs but both markets are susceptible to a cascading failure. The prime example of this would be the 2001 outbreak of foot and mouth disease in the United Kingdom.

So, the livestock farmers in Orkney are part of multiple networks. One could be a small world network and the other a scale-free network. Question that arise include could a small world network be a conduit for a cascading failure? Could the scale-free network loosen the cohesion in a small world network? At this point we do not know the answers to these questions but the answers can help us to understand the ways to establish and maintain resilience in livestock farming in upland areas.

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