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Assuming you have a set of nodes, how do you determine how many connections are needed to connect every node to every other node in the set?

Example input and output:

In   Out <=1  0 2    1 3    3 4    6 5    10 6    15 

3 Answers 3

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Figured it out. The formula is:

x = n(n - 1) / 2 
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If there are $n$ nodes, then this is called "$n$ choose $2$", and is equal to the number of $2$-element subsets of a set of $n$ elements. The Wikipedia article on binomial coefficients includes this and generalizations.

Since I started writing you discovered the correct formula. However, if you ever have a similar problem where you are trying to figure out a general form for the terms in a sequence from some initial values, a good tool is The On-Line Encyclopedia of Integer Sequences. In this case, entering 0,1,3,6,10,15 brings up a useful entry in which you can find the general form and references.

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    That link to oeis.org looks incredibly useful. I was actually looking for something like that, thanks!2011-07-18
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Here is what you want.$\sum_{k=1}^{n-1}k=\frac{n(n-1)}{2}$