This is getting to be very interesting. I was just trying to get up to speed with Graph theory and networks, ended up reading a great article by Valdis Krebs and going through other related articles.
One of the things I was able to put a finger on as I read through the mass of statistical measures on networks/graphs, was that nodes in a social network are not the same e.g. boundary spanners may be critical in a network because they connect groups of nodes, however, they may often be the limiting factor in the growth of the network itself.
I am guessing that perhaps no two neurons would ever behave in the absolutely the same way. But this is perhaps a question left for future research.
But, importantly, think of communication and knowledge flow being inhibited by many frictions. These frictions could be at the nodes or “in the pipes” and play an important role in the efficiency of the flow or the ability to make connections.
Makes me remember the game of Chinese Whispers – the entire group of people spread out in a linear chain with the leader whispering a phrase in the ear of the first person in the chain, exhorting him to repeat the same in the ear of the person next to him and so on. By the end of the chain, the message had distorted many times over!
As another example, navigating a Johari window in a group takes serious and sustained effort. It also requires subsuming many frictions and the capability of the group to be guided and facilitated.
Measuring the strength of ties is important but difficult in practice – e.g. how do you measure trust in a network, if trust fosters effective collaboration? Then again, how does one counter/accomodate human and technological sources of friction among others while measuring strength of ties?