It’s a Small World After All

The reading for this week, Linked by Albert-Laszlo Barabasi, began to outline the concept of networks by highlighting several network theories.

The idea of networks first originated with a Swiss mathematician named Euler.  He lived near a town named Konigsberg which had seven bridges.

The people of the town had always tried to cross all the bridges only once, but Euler offered a proof that it was impossible to cross the seven bridges of Konigsberg without crossing one more than once by laying out vertices at common points.  This spurred the idea of graph theory, which includes “a collection of nodes connected by links” (11).  His graph had nodes that were pieces of land and links that were bridges.  Nodes with an odd number of links must either be the start or end of the journey, and since the graph had more than 2 nodes with an odd number of links, there was no way to only cross each bridge once.

This graph theory spurred several theories about the structure of networks:

1.  Paul Erdos and Alfred Renyi had a theory that social webs form rapidly and randomly.  They “equated complexity with randomness” (23), assuming that all social connections are “fundamentally random” (17).   Despite the links’ random placement, “all nodes will have approximately the same number of links” (22), thus most people have roughly the same amount of friends and acquaintances, no matter how random they may be.

2.  Another theorist was Mark Granovetter, who focused on the “importance of weak social ties in our lives” (41).  He thought that networks were structured in highly connected clusters (close-knit circles of friends) in which everybody knows everybody else along with a few external links connecting these clusters to keep them from being isolated.

3.  A final theory discussed in the reading was one developed by Duncan Watts and Steven Strogatz.  They envisioned that we “live in a circle where everybody knows their immediate neighbor” with random links connecting different people (51).

Which graph theory are you more inclined to believe?  Do you think that our links depend more on randomization or the specific circles we may run in?  Or do you perhaps have your own model in mind?

Another interesting point brought up in the reading is the idea of 6 degrees of separation.  In other words, “people are linked by at most five links” (27).  Anyone in the world can be connected with anyone else through our dense social network.  For example, I will now connect myself with Obama.

1. I went to hebrew school with 2 girls

2. The girls were the daughters of  Lawrence Summers

3. Lawrence Summers was Secretary of the Treasury under the Clinton administration

4. Bill Clinton enjoys lunches with Obama from time to time

Voila!  I’m connected to Obama in 4 links!  I encourage you to see who you can be linked to and in how many steps (George Bush? Kevin Bacon?)

This idea of 6 degrees of separation also carries over to one of the biggest networks in the world; the world wide web. There are billions of pages, with the net growing at an exponential rate. Even so, the connection between any 2 pages on the web is anywhere from 2 to 19 clicks, with an average around 11.

This whole idea of degrees of separation reminded me a lot of Tylan’s posting:

https://idm09.wordpress.com/2009/10/18/space-race/

He talks about something called the wikirace, where people are challenged to find the least amount of clicks to get from one specific topic to the next.  It further illustrates the high level of connectivity between networks, this specifically demonstrating the network of wikipedia pages (which are all interwoven with their many hyperlinks that lead to vast numbers of other pages).