I don't think this is the type of puzzle with "an answer", necessarily. I am interested in how people attack both the average and the maximum. To me they are very different types of problems.
To get people thinking about the maximum length minimal chains between people.
(I will let you double check me)
In a network of 2 people with 1 relationship, the maximum length chain is 1.
In a network of 3 people with 2 relationships, the maximum length chain is 2.
In a network of 3 people with 3 relationships, the maximum length chain is 1.
In a network of 4 people with 3 relationships, the maximum length chain is 3.
In a network of 4 people with 4 relationships, the maximum length chain is 2.
In a network of 4 people with 5 relationships, the maximum length chain is 2.
In a network of 4 people with 6 relationships, the maximum length chain is 1.
In general, in a "path" topology is the worst case for N people with N1 relationships, with the longest chain, of length N1, being between the two "ends".
In general, in a "clique" topology, where everyone knows every one, the longest length chain is 1. For N people there needs to be Chose(N,2) relationships for clique. That is N(N1)/2 relationships.
For 7 billion people, to form a clique would require almost 25*10^18 relationships, far more than the 4 trillion estimate.
So you can bound the length of the maximum minimal path to be between 2 and 7 billion. Not much of a bound.
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09092011, 09:54 AM #11
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

09102011, 10:56 PM #12INtp
5w6 or 9w1 sp/so/sx, I think
Ravenclaw/Hufflepuff
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LIINe

09122011, 11:10 PM #13
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
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