Six degrees of separation

Last week there was a news item about the connectivity of the Facebook universe. 
"Researchers at Facebook and the University of Milan reckon that the degrees of separation between any two people in the world have been reduced to 4.7 from social psychologist Stanley Milgram's "small world experiment" of six back in the '60s.
The study which measured how many friends people have on Facebook, found that the notion of six degrees of separation had been shrinking over the past three years at the same time as the dominant social network bumped up its userbase.
It also noted, unsurprisingly, that many of those connections are localised."

Graphs and networks are an important component of the mathematics of Operational Research, and it is interesting to see some of the statistics of the Facebook graph.  Newspaper reports have focussed on the statistic that the average separation is 4.7 on Facebook.  Reading the fuller report, two further statistics  have struck me.  The first is that the Facebook graph is almost wholly one component.  Over 99.9% of active Facebook users are connected to one another through friends of (friends of) friends.  (Repeat the (friends of) as many times as needed.)  Such is the dominance of this "super component" that the next largest component has about 2000 Facebook members.  The second is that most Facebook friends are local in both space and age.  It is hardly surprising.  True, my Facebook friends include some people in other countries, but the majority are in the UK, and a significant number are in my home city of Exeter.  And most are of a similar age to me ... a few family members are a generation younger.

Now I am waiting for someone to calculate degrees of separation across time.  If my parents and grandparents were connected by six degrees of separation to the world when they were my age, then it only takes seven degrees to separate me from their world.  Taking this further, each grandparent adds another degree, say sixty years per degree.  William Shakespeare died in 1616, about 400 years ago.  That makes six or seven time steps ... twelve or thirteen degrees of separation between me and the Bard?

I started this train of thought because of a coincidence.  In another blog, I wrote about a street in Exeter which was completely destroyed in the Exeter blitz of 1942.  St Leonard's Terrace was never rebuilt.  My late great-aunt's book collection, some of which I have inherited, included her contributions to a trivia column in a newspaper, "The Daily Post".  The column published one or two thoughtful quotations each day ... and one of my great-aunt's appeared alongside one from a resident of St Leonard's Terrace in 1932.  They certainly never met, but had that fleeting moment when they appeared in the same issue of the paper.  And so I have a flimsy link to the street which was blitzed.


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