I wonder why people consider “social networks” to be a “new thing”. It’s the “rage these days”, they say. Actually, they’ve been around for a while but in a different disguise.

Take the case of the Erdos number:

In order to be assigned an Erdos number, an author must co-write a mathematical paper with an author with a finite Erdos number. Paul Erdos is the one person having an Erdos number of zero. If the lowest Erdos number of a coauthor is k, then the author’s Erdos number is k + 1.Erdos wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators; these are the people with Erdos number 1. The people who have collaborated with them (but not with Erdos himself) have an Erdos number of 2 (8,162 people as of 2007), those who have collaborated with people who have an Erdos number of 2 (but not with Erdos or anyone with an Erdos number of 1) have an Erdos number of 3, and so forth. A person with no such coauthorship chain connecting to Erdos has no Erdos number (or an undefined one).

There is room for ambiguity over what constitutes a link between two authors; the Erdos Number Project website says “Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted,” but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The “Erdos number of the second kind” restricts assignment of Erdos numbers to papers with only two collaborators.

…

Erdos numbers have been a part of the folklore of mathematicians throughout the world for many years.

Amongst all working mathematicians at the turn of the millennium who have a finite Erdos number, the numbers range up to 15, the median is 5, the average Erdos number is 4.65; and almost everyone with a finite Erdos number has a number less than 8.

So, Erdos numbers is essentially a social network that counts the degrees of separation.

Somewhat relatedly, there is also an interesting theory called Dunbar’s number:

Dunbar’s number is the supposed cognitive limit to the number of individuals with whom any one person can maintain stable social relationships: the kind of relationships that go with knowing who each person is and how each person relates socially to every other person.Dunbar has argued that 150 would be the mean group size only for communities with a very high incentive to remain together. For a group of this size to remain cohesive, Dunbar speculated that as much as 42% of the group’s time would have to be devoted to social grooming.

I wonder what would be the Dunbar number of the social circles that I know of.

Thanks for bringing up such a nice topic swaroop :)

Since your post is about the social network or the so called “Small World” problems thought I would add one more person who has been a major inspiration for researchers in this field.

Actor Kevin Bacon has been one of the prominent person who has been associated a lot with the small world problems among the research community. There is also a Bacon number which tells how far are other actors associated with him in the industry. Average Bacon number is 2.946 [4]

There is also a number called “Erdos-Bacon” number which measures the distance of actor-mathematician or mathematician-actors with them.

Below are some links about the same.

[1] http://en.wikipedia.org/wiki/Small_world_phenomenon

[2] http://en.wikipedia.org/wiki/Erd%C5%91s-Bacon_number

[3] http://en.wikipedia.org/wiki/Six_Degrees_of_Kevin_Bacon

[4] http://www.oracleofbacon.org/cgi-bin/oracle/center-cgi?who=Kevin+Bacon

@RaviShankar Wow, I had observed references to Bacon in many places including internal project code names in Adobe, but now I know why Bacon is the center of the universe!

Nice reading all the articles. But I wonder if we’ll ever get to the stage where social interaction is actually enhanced by the application of such theories (and others) in practice. Untill now, Facebook, MySpace and all other existing networks have a very simplified form of social interaction that is quite unlike the real world. Of course, when I say this, I don’t mean ranking friends according to most important, important and not important, I mean a system that allows you to discover and interact in a seamless way without constantly asking you about your relationships. I guess this is also related to the Semantic Web in some way (computers being able to understand data, content and relationships).

@Abi I agree that the existing way it works is unnatural, but I’m not sure how you would apply these theories to better “social networks.”

In the era of everybody thinking that the social media is the new cool dude around the block, you have definitely brought a different perspective to this.

I thoroughly enjoyed reading this article.

~ Ramesh

Voicing everyone again, a very interesting article Mr Swaroop.

As “ABI” has commented (and wondered)on “the stage where if we’ll ever get to the stage where social interaction is actually enhanced by the application of such theories (and others) in practice.” , I myself am wondering if those people on the social networking sites with a high Dunbar’s number can be a target for “viral marketing”.

These people can be the target of companies selling products or applications specifically catering to these people’s likes and wants.

And since these people with a high Dunbar’s number efficiently communicate with like-minded people around them, the said product or application finds it’s way into the hands (computer screens, in fact) of right people, thereby decreasing spamming.

What do you say?