I'm reading Mark Buchanan's excellent book on Small Worlds and the Groundbreaking Theory of Networks, and came across the concepts of egalitarian and autocratic patterns in social networks. Before you jump to conclusions, let me say a few things about this book. To me it seems to focus on the mathematical origins of the theory of social networks, but takes a pleasant approach going through the history and background of how these ideas emerged. It also spans a wide range of disciplines in terms of where these patterns appear, from biology to watershed and geological studies.
First, it talks about Watts and Strogatz's truly innovative look that has eventually spread across the world as the meme: six degrees of separation. There's a lot more to it than the Kevin Bacon game, but I'd like to point out the particular elements here on egalitarian and autocratic networks. This is actually has little to do with policital systems like socialism versus monarchic or oligarchic communities. Instead if you look at it as a mathematical problem, what it describes is that there are often two varieties of patterns of connections in a system that emerge often.
The first is a basic heuristic that can be commonly seen in some biological systems like the brain: as a node (in a network system), you try to establish a fixed amount or ratio of connections to other nodes. The connections are not a random pattern, but neither is it based on a high degree of "purpose" or "intention". This proposes a very egalitarian and essentially a very simple rule to help build more complex systems as the overall network grows and evolves.
The other is the autocratic pattern, where the heuristic is to start with one node and grow from there. Essentially the key node itself starts growing in size or strength, while its immediate connections grows with it, and scaling down until you reach the end or leaf nodes which have only one connection to someone else. This easiest example is in terms of well known sites or articles on the Net that get linked from many sites, and in a very simplified description, the basis of the algorithm that Google's engine uses.
If you look at one example of each of these networks from a high level, the egalitarian network seems to be completely chaotic with no easily discernable pattern you can tell visually. On the other hand, the autocratic network looks strangely like one of those classic fractal diagrams. Yet, both serve different purposes and have different uses. You might almost say that they are the yin and yang that exist pervasively throughout the world. Okay, maybe that's too metaphysical for a Friday :)
Egalitarian and Autocratic networks