So I just watched Connected: The Power of Six Degrees, a Science Channel show on network theory. It seems the whole thing is Kevin Bacon's fault. It is a good recap of the six degrees of separation with some pretty common sense stuff if you just stop to think about it. For example, most social networks are fairly homogeneous and rather small. These would be considered local clusters. Interconnecting local clusters has a profound impact on the transmission of information.
Most of it does seems to be common sense. Consider a native tribe using drums or smoke signals. In this way local clusters - the tribe - could signal another cluster (again tribe) about important events - perhaps the location of buffalo, or impending invaders. This kind of information transmission has been going on for a long time. Modern day examples are the telegraph, telephone, and of course the internet.
The show also discussed the importance of hubs - points of massive connectivity - and their importance, for example removing hubs can cause a network to collapse. I couldn't help but think that the television I was watching was a kind of hub. I thought about CNN and the other news channels, each of which leans this way or that, each of which feeds information from their distribution hubs into our little local clusters. Kind of a Babbit thing.
The notion of a hub, though, is not new either. Trading posts were hubs as were the first towns and cities. They were certainly larger than the local village (family) cluster! Over time they took on ever important roles, stripping the family cluster of it's independence, and perhaps even lording over the clusters (families) within their reach.
The list is endless, universities are hubs of learning, a nation is a cultural hub, and so on. An organization is certainly a hub, a center of activity that, as we have seen lately, can disrupt many clusters (again families) if it runs itself into the ground.
There are an interesting implications to self organization and adaptability. When the connections between the nodes of a network are too low, the network is overly stable and while stability seems like a good thing, it isn't when adaptability is required. Self organization and adaptability seems to occur spontaneously when all the nodes of a network have two connections.
In such a network, the number of possible states is 2^N or two to the power of N where N is the number of nodes in the network. In large networks the number of possible states can be staggering. The thing here is that when the connections is equal to two, a system settles into a relatively few number of states (behavioral patterns), which approximates the square root of the number of nodes. This is self organization. These systems are adaptive and able to withstand perturbation through reconfiguration.The classic example cited is DNA.
Our DNA has, perhaps between 65,000 and 75,000 genes. The number of possible states is 2^100,000 (a very big number). If we take square root of 65,000 (our self organizing pattern equation) we have just 256 possible states for our DNA to assume. Biologists tell us that we have somewhere around 250 or so cell types. Not too bad.
Anyway. I need to noodle on this more because as we all know social networks - facebook, myspace, and linkedin, to name a few, are all perfect examples of networks with local clusters and massive hubs.
Watch the show, its on one more time.
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