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6 degrees of separation (or network theory)

June 5th, 2009 · No Comments · web 2.0

I watched a fascinating programme on BBC TV tonight called Six Degrees of Separation.  I decided to watch it again on the BBC iPlayer and make notes in order to post on it in some detail later. Unfortunately it looks as if it will not be available to play again. So I thought I would jot some notes here anyway before I forget and try to follow the ideas up later via other sources. It seems that ‘small worlds’ connect to big worlds via a small number of connections. Only a comparatively small number of links between small worlds has the effect of shrinking the whole network significantly. This seems to be a universal feature of all real world networks. These fairly few interconnections through which most traffic passes are called ‘hubs’. Apparently there is a mathematical formula that tells us how many hubs in a given network are likely to exist. A network can survive any amount of nodes/connections being destroyed but not if hubs are destroyed.  Using the WWW and page linking as an example, the scientist in the programme said you would assume that the distribution of pages and the number of links they have made to them would be a normal distribution, a few with no links to them perhaps, a few with a 10s of thousands or more links to them but the majority clustering symmetrically round a mean number of links. I don’t know why we should assume that, but he said we should. However, on inspection it seems the distribution is highly skewed with a very small number of sites with massive number of links to them (i.e. Google, Amazon, etc.) and a rapid fall off and very long tail of millions of pages with very few links to them, down to zero. This is what I would have expected, but then I’m obviously a bit weird. The point is that if one of these hubs goes down very many small word connections go down with them.

The 6 degrees of seperation refers to the notion that, pick any living individual in the world, you will only be a chain of 6 people who know people who know him or her.  This was tested in the programme by identifying a Prof in Boston USA and giving 40 packages to random people all over the globe. They had to pass the package on to someone who they felt might have some chance of knowing the Prof or at least knowing someone that might know someone (and so on) that might know the Prof. For a woman in a village in Uganda it turned out to be a relative who knew someone in the US. The programme followed this package and sure enough it was eventually handed to the Prof by someone who was known to someone known to someone (and so on) who new the original woman in the Ugandan village.  All dramatic stuff until at the very end of the programme they quietly mentioned that only 3 of the 40 packages got through! This was the result of  a similar experiment reported by the BBC on August 2008 – Study revives six degrees theory.  However, what are the implications of this for learning and research networks? Well the good news is that I am  probably only 6 steps away in a  potential communication chain with the best brains on any subject you care to mention. The bad news is I have no idea how to tap into that brain via this chain. I may as well just email the expert in question directly and ask a question. I think the notion  of hubs may be more interesting in practical terms. Who or what site in an expert’s small world makes the expert’s knowledge available. I think this is common sense really. If you want to know what current thinking is on, say, network theory, or connectionism (George Seimens) then who’s doing the research, who is reporting on it, summarising it, discussing it? There’s your hub. There is your link into the smaller experts’ network of expertise.  It is obvious, I think, how important are digital presence and reputation in these matters. It is these plus exposure, a willingness to do business in public, that creates the hubs of learning and research networks. Thank goodness for these people. Without them my personal learning/research network would be in serious trouble. One question might be, why do they do it? Some for PR and marketing perhaps, some because they explicitly want to build a digital presence and reputation perhaps. For many I am sure it is because their followers are part of their learning/research networks from whome they feedback, comments, discussion, sharing ideas and resources. It also allows a powerful mixture of formal, informal, serendipitous (!) and vicarious learning.


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