Power Law and Social Media

I spend a lot of time with a biochemist, who is in love with proteins. Really. He spends more time fondly thinking about proteins, their structures and activities than anything else. Yes, there is debate about such things, and, yes, proteins actually do stuff. I am a little sad I know this.

Anyway, this perhaps explains why a particular passage in chapter 3 of Jill Walker Rettberg’s Blogging jumped out at me:

Simply put, the power law states that blogs that already have ‘power’ will get more. This is not a feature specific to blog or social networks; it is a feature of networks, as physicist and network theorist Albert Laszlo Barabasi explains:

A new node joining a network, such as a new web page or a new protein, can in principle connect to any pre-existing node. However, preferential attachment dictates that its choice will not be entirely random, but linearly biased by the degree of pre-existing nodes — that is, the number of links that the nodes have with other nodes.  This induces a rich-get-richer effect, allowing more connected nodes to gain more links at the expense of their less-connected counterparts.  Hence, the large-degree nodes turn into hubs and the network becomes scale-free — the probability distribution of the degrees over the entire network follows a power law. (Barabasi 2012)

So much for the freedom and egalitarianism of the web.

I have to admit, I did not understand all of the jargon in the above passage.  What the heck does scale-free mean? The image it brought to mind was fish scales.  Probably because I was hungry.  Luckily for me, I have the hub known as Google.  I found a nice (albeit lengthy and academic) Scientific American article through the University of Notre Dame’s website. Basically, previous theories looked at networks as random — each node in a random system has an equal number of connections to other nodes. Okay, then they studied the Internet. Barbasi and Bornabeau write:

So in 1998, when we, together with Hawoong Jeong and Reka Albert of the University of Notre Dame, embarked on a project to map the World Wide Web, we expected to find a random network. Here’s why: people follow their unique interests when deciding what sites to link their Web documents to, and given the diversity of everyone’s interests and the tremendous number of pages they can choose from, the resulting pattern of connections should appear fairly random. The measurements, however, defied that expectation. Software designed for this project hopped from one Web page to another and collected all the links it could. Although this virtual robot reached only a tiny fraction of the entire Web, the map it assembled revealed something quite surprising: a few highly connected pages are essentially holding the World Wide Web together. More than 80 percent of the pages on the map had fewer than four links, but a small minority, less than 0.01 percent of all nodes, had more than 1,000.

That was in 1998, when the world wide web was a bit smaller.  In 2005 it looked like this:

OPTE Projet Map of the Internet 2005

They called these systems “scale-free” to reflect the fact that some nodes, or hubs, have a seemingly unlimited number of links and no node is like any other.  Apparently these types of networks can be found everywhere, from cell’s metabolic systems to actors in Hollywood. In these systems a small percentage of nodes have the most connections and keep it all together.  Apparently these systems behave similarly — they are pretty immune to accidental disaster, but vulnerable to planned attack.  hmmmmm …

I also found this Popular Science article on Albert-Laszlo Barabasi which was interesting and frightening, all at the same time.  On page 2 Gregory Mone, the author of the piece, gets into Barbasi’s more recent work with “control nodes.” He has been studying just what percentage of hubs need to be manipulated in order to change, or control, a system.

Yikes.  I suppose this can be a good thing in terms of proteins and tumor growth, but the idea that a small percentage of websites are control nodes in the system of the internet, well, that is troubling.

On a lighter note:

This video is fun.  It is a look at how we see the world — the shift from the hierarchy of the tree to the power of networks:

There is more to say about all of this — beyond the research into what the theory is.  Hopefully I can wrap my brain around it and write more about it in another post.