Carl Zimmer's National Geographic article, "The Parts of Life," merits reading -- and rereading. The structure of networks, meaning their level of complexity, is difficult to understand but Zimmer moves carefully to lay out an experiment conducted by Jeff Clune (University of Wyoming), Jean-Baptiste Mouret (Pierre and Marie Curie University, Paris), and Hod Lipson (Cornell University). If I've got this right, their experiments indicated that "minimally-linked networks spontaneously produce[s] modules."
Why is this important? Modules are the basis of life -- parts make up wholes, what Jeff Stamps talked about in his book, Holonomy, drawing on Arthur Koestler's elegant term holon, meaning whole-part. As Zimmer says:
We’re made of parts. Our skull is distinct from our spine. Our liver does not grade subtly into our intestines. Of course, the parts have to be connected for us to work as a whole: a skull completely separated from a spine is not much good to anyone.
This is obvious in physical and biological systems, viz. see Herbert Simon's classic, "The Architecture of Complexity." But what about social systems? Do minimally linked networks/organizations spontaneously produce modular groups of mini-networks that can specialize to solve problems?
What is just-the-right-number of links to produce just-the-right-kind of modules to get work done? Complexity scientist Stuart Kauffman has written about this, postulating that there is some apt number of links to create that "place" between order and chaos. See this white paper that we wrote some time ago, "Organizing at the Edge of Chaos," which plays with the tradeoff between too many links and too few in organizations.