It’s a small world after all

Morgan Freeman’s Bacon Number is 2. He appeared in Wanted next to James McAvoy, who appeared next to Kevin Bacon in X-Men: First Class. Thus, Morgan Freeman is only two degrees of co-actorship away from Kevin Bacon.

According to the six degrees of Kevin Bacon, no Hollywood actor or actress is separated by more than six co-actorships from Kevin Bacon. This, of course, is a clever variation on the six degrees of separation, a theory which says everyone in the world – including you, the Pope, and Barack Obama – is connected on average by only six people.

Both the six degrees of separation and the six degrees of Kevin Bacon can be explained by small-world networks.

In a small-world network, every single entity is described as a node, which can be connected to other nodes with a tie. Some nodes only have one tie, others have a lot; nodes with many ties are referred to as hubs. A node may not be tied directly to another node, but the distance between two nodes will always be small because the hubs link all nodes together.

Examples of these small-world networks can be found and mapped in many forms of social networks. The most obvious ones include networks from social media like Facebook and LinkedIn.

LinkedIn network of DJ Patil (former chief scientist at LinkedIn). Made using InMaps.

A less obvious example is a network of sexual relationships, which can be mapped using questionnaires. Mapping these kinds of networks is useful in investigating the spread of STDs.

A sexual network associated with an STD outbreak. Sexually Transmitted Infections, Potterat et al. doi:10.1136/sti.78.suppl_1.i152

Interestingly, clusters tend to form of people with similar lifestyles and emotions. These clusters extend to three degrees of separation.

That means that if someone is obese, that will increase the chance of their friends, their friends’ friends and even their friends’ friends’ friends of being obese. Your way of living has a big impact on your surroundings.

A social network in which clustering of body weight is visible; node size corresponds to body weight, yellow nodes depict a BMI ≥30 (obese). The New England Journal of Medicine, Christakis & Fowler doi:10.1056/NEJMsa066082

Small-world networks can be found in areas other than social networks – from areas with an enormous scale such as the internet to small biological systems like gene interactions and neural networks.

What would be the evolutionary benefit of a small-world network in biological systems? Of course, when the network is intact, the distance between two nodes will always be small because of the hubs.

But think of what happens when a random node shuts down. The answer is: not a lot. Small-world networks are extremely resilient to random damage – as long as the hubs remain intact, the distance between two nodes will remain the same, and the network will be able to function properly.

As you can see, from Morgan Freeman and Kevin Bacon to the internet and to your genes – everything is connected by a small-world network. Indeed, it’s a small world after all.

4 Responses to “It’s a small world after all”

  1. Jan Koeleman says:

    @Harriet, you’re right, research has actually been done on small-world networks in memory!

  2. Scott Lillie says:

    Very cool post! The obesity relation is pretty amazing. Awesome diagrams.

  3. Harriet Dashnow says:

    Very interesting stuff. I imagine these ideas could be applied to semantic memory networks, to explain how neurons are connected.

    The data out of the Framingham heart study sure has been put to some pretty interesting use!

  4. S.H.W. says:

    Great post! I had a look at the facebook network link and that’s pretty incredible.