The formula I have been using is a combination.
http://en.wikipedia.org/wiki/Combination

That is n!/(k!(n – k)!) where n is the number of elements and k is the number of items in the set.
There are two people in a line of communication, so k is always 2 for this example.
2! = 2 * 1 = 2
2!(2-2)! = 2 * 1 * (1) = 2
2/2 = 1 line of communication

Note: Factorial of 0 = 1

6 people?
6! = 6*5*4*3*2*1 = 720
2! (6-2)! = 2 * 1 * (4)! = 2 * (4*3*2*1) = 2 * (24) = 48
720/48 = 15 lines of communication

4 people?
4! = 24
2! (4-2)! = 2 * (2) = 4
24/4 = 6 lines of communication

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Great message, but one pedantic note: n(n-1)/2 is O(n^2) and hence a polynomial function of degree 2, not an exponential one. Of course, this is still pretty fast, but nothing like exponential growth!

As I understand it, exponential functions are those where the dependent variable appears in a *power* in the formula. For example O(2^n).

A better model for team size might perhaps be a hyperbolic tangent, where the marginal cost of adding team members is low when teams are very large or very small, but approximates O(n^2) as teams grow from small to mid-sized.

This reflects that as teams get large you adopt mechanisms for communication and coordinating that are more appropriate for these larger team sizes, even though they are considerably less effective. Examples are the use of wikis that everyone can access rather than information stored on whiteboards and email communication rather than personal ad-hoc meetings.

This is all pretty theoretical and doesn’t change your message, but I felt I should throw it out there anyway as it’s kind of an interesting line of thought.