How do you calculate the number of links between hubs?

Factual Questions
1

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.

2

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.

3

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.

4

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.

5

You’re describing a complete graph, and there’s lots of information at the link.