# How do you calculate the number of links between hubs? **URL:** \ **Category:** Factual Questions\ **Created:** [October 10, 2010, 2:09am UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651 "2010-10-10T02:09:57Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![MichaelEmouse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/michaelemouse/32/101_2.png) [@MichaelEmouse](https://boards.straightdope.com/u/MichaelEmouse)\ **Post date:** [October 10, 2010, 2:09am UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651/1 "2010-10-10T02:09:57Z")
So, if I have 1 dots, I can make 0 links. 2 dots=1 link (1 additional). 3 dots=3 links (2 additional). 4 dots=6 links (3 additional). 5 dots= 10 links (4 additional). 6 dots = 15 links (5 additional). Is there a formula or a website that can help me calculate the number of links for any number of dots? Is it always one more link than the previous number of added links / one less additional link than the number of dots? Relevance: Some thoughts I have about increasing marginal returns/the network effect. ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [October 10, 2010, 2:31am UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651/2 "2010-10-10T02:31:03Z")
For n dots you should have nC2 links, or n!/(2! \* (n-2)!). That doesn’t line up with your series, so perhaps I’m misunderstanding the question. Are you asking for n dots, how many lines can I draw between dots without repeating a combination of dots? Edit: Never mind, it does line up. That is the correct formula. ---
**Author:** ![MichaelEmouse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/michaelemouse/32/101_2.png) [@MichaelEmouse](https://boards.straightdope.com/u/MichaelEmouse)\ **Post date:** [October 10, 2010, 2:34am UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651/3 "2010-10-10T02:34:38Z")
> [@Rysto](#): > > For n dots you should have nC2 links, or n!/(2! \* (n-2)!). That doesn’t line up with your series, so perhaps I’m misunderstanding the question. Are you asking for n dots, how many lines can I draw between dots without repeating a combination of dots? Yes, I am asking how many lines I can draw between dots without repeating a combination of dots. I just drew dots and links on a piece of paper so I could very well have gotten 5 and 6 dots wrong. ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [October 10, 2010, 2:38am UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651/4 "2010-10-10T02:38:46Z")
And now that I am thinking again, that formula reduces to n \* (n - 1) / 2. As that is a quadratic then its derivative will be linear, so the rule that you noticed(the difference between each step will be one greater) will hold. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 10, 2010, 6:01pm UTC](https://boards.straightdope.com/t/how-do-you-calculate-the-number-of-links-between-hubs/556651/5 "2010-10-10T18:01:08Z")
You’re describing a [complete graph](http://en.wikipedia.org/wiki/Complete_graph), and there’s lots of information at the link.