Archive for the 'Networks' Category

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Random Wiring Redux

Published on December 18, 2005 in Networks, Research and Simulation. 0 Comments

In a previous post, I wrote about Stuart Kauffman’s thought experiment on the emergence of a giant component in a randomly wired network, then linked you to a very rudimentary simulation I coded. Now I just found a very elegant version of the same model, complete with dynamic visualization of the network as it grows. As of September 2005, it’s now included in the standard Model Library that ships with NetLogo. I’m impressed that NetLogo can do spring-elastic network layout like the more powerful but user-unfriendly Pajek. Of course, Pajek is a network-specific analysis tool while NetLogo is a far more general purpose simulation package.

So go try out the new Giant Component model. (Java applet)

How to sew like Stuart Kauffman

Published on November 28, 2005 in Networks, Research and Simulation. 3 Comments

In his book, At Home in the Universe, my colleague Stuart Kauffman describes a simple model of random network formation.

Imagine dumping a box of buttons (as in shirt buttons) onto your floor. Now pick up two buttons at random, tie them together with thread, and put them back down. You now have one connected component of two buttons and N-2 singleton buttons. Repeat. Over time, when you pick up a random button it will become more likely that it will lift up a small group of others with it. The interesting thing is, as the number of threads approaches one-half the number of buttons, a single, massive connected component will suddenly emerge such that when you pick up a random button, it is very likely to lift the vast majority of the other buttons. In other words, there is a critical phase transition as the system suddenly shifts from a collection of many, small, isolated groups to a single monolithic group, plus a few outliers.

To demonstrate this phenomenon, I just created a NetLogo simulation of Random Button Networks (Java applet), after following an introductory tutorial at the Complexity Workshop. Enjoy.

Random Button Network Simulation (Java applet)

When do networks not matter?

Published on November 18, 2005 in Networks, Research and Science Culture. 0 Comments

The question may have never occured to network researchers and enthusiasts. When you’ve found a paradigm that you love, it’s hard to see the boundaries of its utility. It’s the old “when you have a hammer, everything looks like a nail” story. But actually, the question which titles this post is an important networks question — not just a caution against overzealous methodologizing — because knowing when the network doesn’t matter means knowing when it does.

Network analysts use random networks as the standard by which to measure order in the networks they study. That’s because a random network is the graph-theoretic way of saying structure doesn’t matter. If the network structure you’re studying is significantly different from the random net, most likely it can’t be explained by chance alone; it has order, pattern, maybe even complexity. In other words, for the purposes of studying whatever system produced that structure, the network matters, i.e. it’s worth paying attention to.

And in the games of life and science, what matters most is knowing what is worthy of your thought and attention, and what is not.