"Giant Components" Implies WInner-Takes-All in the Social Network Race

In graph theoretic social networking analysis, there's a concept known as "Giant Components". As the name implies, in any given human social network, there exists one main, extremely large, set of connected "nodes" (people) surrounded by significantly smaller, disconnected from the giant component, peripheral clusters of social networks.

This is illustrated qualitatively in "Networks, Crowds, and Markets" (free version here) by given the example: consider your current friend group, and who they're connected to, and so on. Ultimately, you'll find you're indirected connected to people from other countries. Another way to put it, if everyone has 100 (unique) friends, you very quickly get to large numbers of connected nodes (100 of your friends x (have) 100 friends x (who have) 100 friends x (who have) 100 friends x (who have) 100 friends = 10B people. However, there will be people, isolated on an island somewhere, that is not connected to the giant component.

Random Example (from here). You can see that a high proportion of nodes below to one connected cluster.

If any one person, in any one of the smaller clusters, becomes connected to the "Giant Component", the entire cluster is then considered part of the "Giant Component". So, it's reasonable to assume that, at some point, the desert island person will eventually meet one person in the giant component. It seems, in this connected world, we're almost fatalistically destined to be part of the giant component.

It is inevitable then, that we become part of the Facebook giant component, right? They're nearing 600 millions users, and check out this giant component.

In reality, things aren't as inevitable. It's not obvious initially, but a few things to consider:

• The definition of the edges (connections between people) are a little more nuanced than simply "knowing" someone. What if you, instead of drawing a social graph based on Facebook-stated friendships, you drew it based on spending greater than 10 hours a day together? The graph would become much more fragmented.
• Graphs can be used to represent different classes of social graphs. For example, and Facebook even does this, my family, and my coworkers could be represented as separate graphs. In other words, people are capable of belonging to multiple networks.

Both of these facts create an opportunity for emerging or niche social networks to evolve and grow -- and not necessarily at the expense of Facebook either! In retrospect, Livemocha, an interest-based social network, benefited from this.

Another example (or maybe a 3rd bullet is required above stating "cultural norms") is Mixi, a Japanese social network. Recently featured in the NYTimes, Facebook has been relatively unsuccessful in Japan. Some speculate it is cultural in nature; that the Japanese are more private and that Facebook's religious-like fervor towards unfettered openness doesn't resonate there. Allegedly, on Mixi only 5% of users use their real picture as an avatar.

The "giant component" question seems to simply be one of definition. Existentially, or environmentally, aren't we all connected?

As an aside, I'm taking a Social Media Analysis reading course this semester (similar to this one at Carnegie Melon). I have a weekly blog-writing assignment - this is the first post of many.