# Thread: How Small is the World? Socially Speaking

1. 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 N-1 relationships, with the longest chain, of length N-1, 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(N-1)/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.

2. Originally Posted by SuchIrony
Yeah, I have heard of the idea. But how do they work out 6 on average? ...and what would be the maximum?

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