Andre Durand conjectures that the network is collapsing (in the sense that nodes, be they devices or people, are more easily connected than in the past). With the help of his mathematician father, he explores the rate of collapse, e.g. from year to year how much closer are the nodes. Interesting stuff.
As a starting point, they use what they call 'Kevin Bacon's 6 Degrees Theory'. Problem is, I don't think there is such a theory - this expression conflates two different ideas of small-world research.
The first is the well-known '6 degrees of separation' theory - the idea that anyone on the Earth can be connected to any other through a chain of at most 5 acquaitances. The second aspect is a game called 'Six Degrees of Kevin Bacon' in which Hollywood actors are labelled by their 'distance' from Kevin Bacon, this determined by how many links there are in the chain of co-actors between them and Bacon. So, different actors are said to have different 'Bacon numbers' (just as mathematicians can be labelled by their Erdos number)
But, as far as I know, there has never been a conjecture that the number 6 is in any way special for the Bacon number. A variety of actors will have this for a Bacon number, but many others will have Bacon numbers of 5 and 7.
It's meaningful to explore either the possibility that '6 degrees of separation' is becoming '5 degress of separation' (likely but by no means certain) or the possibility that a given actor's Bacon number decreases over time (it can't get larger) - but seems to me that Andre and his father are trying to combine the two.
Maybe we should define a Cameron Number, e.g. how distant people are from Microsoft's Kim Cameron - this distance defined with respect to blog roll membership (among other possible criteria like shared conference attendance). I don't personally know Kim but nonetheless have a Cameron Number of '2' (thank you Pat Patterson).
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Actually, if we're talking about the "Identity Cluster", then we're all 1 degree from Kim, who is what I call, a 'super-node'. I suspect the rate of collapse was pretty intense in this cluster.
What would be interesting to know, and what I could not get my father to put forth any sort of conjecture, is the rate of collapse between any and all two end-points.
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