Anyway, I agree with you that scale-free networks do not have all the characteristics of P2P, as you and others envisage them. Though they are quite decentralized, they do feature an “inequality of distribution”. Though the great majority of nodes are about equal in their importance (if we equate importance with connectivity), a few are much more important than others. The fact that personal wealth distribution in the West seems to follow closely a scale-free distribution really tells us all we need to know.

However, scale-free is certainly not the last word in network theory. For example, studies of the internet’s organization, which contribute by far the most to our understanding of networks, have shown that while large portions of it are well-modelled by scale-free behavior, other portions are not. I’m not sure how one would describe these other portions, I’m not sure the people who study these things know, either. But something else seems to be going on, and as the internet continues to expand, and as studies of it also do, we may have a better idea of these other kinds of organization, and their relationship to the development of scale-free systems.

Another point to keep in mind, one I did make in my article on the subject at Visser’s site, is that there are other kinds of organization found in the natural world. It does seem that scale-free is just one kind that appears at certain regular times during development. Thus we see it in the metabolic networks within cells; (probably) in the neural pathways of the brain; and in complex human societies. In my model, these all represent the highest stages of development at a particular level of existence. They appear just as a new level of existence is about to emerge. Development of this new level, though, does not follow scale-free dynamics. In that article, I mentioned other kinds of organization that seem to be more characteristic of early stages of development of new levels, and the examples I gave should not be considered exhaustive.

Having said all this, though, I want to emphasize that I think scale-free organization is extremely important to modern human societies,and that this is not going to change for a long time. While we all have our notions of how society “should” be organized, I think we do have to keep in mind that what actually develops is vastly larger and more complex than any of us, and is likely to follow laws that are to a large extent beyond our manipulation. At this level, we are not talking about molecules or cells that we can manipulate in a laboratory. We are the units, and the very fact that we have certain desires about how society should be organized is itself part of the properties of the system that the final organization reflects. We may think that we are actively trying to change our destiny, but I would say from the point of view of the larger system in which we are all embedded, our efforts to this end are just the natural consequece of units or nodes with certain properties interacting with other nodes with other properties.

In other words…human thought is not the highest form of life. From some higher point of view it may just be another phenomenon that manifests itself in the forms and content that it does because of its relationships to other phenomena. From our point of view, it may appear that we are freely creating new ways of relating to each other, when in fact we are simply along for the ride, with the creation determined by forces beyond our control.