280 15 Emergent Networks of Intelligence
15.2 Small World Networks
One simple but potentially useful observation about CogPrime Atomspaces is that they are generally going to be small world networks [Buc03], rather than random graphs. A small world network is a graph in which the connectivities of the various nodes display a power law behavior — so that, loosely speaking, there are a few nodes with very many links, then more nodes with a modest number of links ... and finally, a huge number of nodes with very few links. This kind of network occurs in many natural and human systems, including citations among papers, financial arrangements among banks, links between Web pages and the spread of diseases among people or animals. In a weighted network like an Atomspace, "small-world-ness" must be defined in a manner taking the weights into account, and there are several obvious ways to do this. Figure 15.1 depicts a small but prototypical small-worlds network, with a few "hub" nodes possessing far more neighbors than the others, and then some secondary hubs, etc.
An excellent reference on network theory in general, including but not limited to small world networks, is Peter Csermely’s Weak Links [Cse06]. Many of the ideas in that work have apparent OpenCog applications, which are not elaborated here.
Fig. 15.1: A typical, though small-sized, small-worlds network.
One process via which small world networks commonly form is "preferential attachment" [Bar02]. This occurs in essence when "the rich get richer" — i.e. when nodes in the network grow new links, in a manner that causes them to preferentially grow links to nodes that already have more links. It is not hard to see that CogPrime’s ECAN dynamics will naturally lead to
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