hey, it’s scale free and … and …
A focus of network research since, say 1999 or so, has been to identify “laws” that generate large networks with certain properties.* For example, the small world network is built by rewiring a grid. Various processes generate power-law networks (i.e., the node distribution is described by a power law).
I can see two justifications for this type of research. The first is diffusion theory. The speed at which something diffuses in a network is definitely governed by the structure. The second is a sort of physical science justification, where you think of a network as a “system” and you show that some micro-process (e.g., preferential attachment) creates that network.
Is there any other behavioral implication of studying power laws/small worlds or other specific large scale properties? In other words, why should I care about scale free or small world networks aside from diffusion theory?
* Let’s leave aside recent criticism of power-law centric research for the sake of the post.