Network graph: Given a network of n nodes, how to assign each node exactly r bidirectional connections?

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I am a bit ashamed to ask this question. I work as a programmer, but my math is horribly bad.

It's not a programming question, as it's more related to graphs than actual code, that's why I decided to not ask in stackoverflow.com

I assume this should be trivial for people in here...?

Given a network of n nodes, is it possible to assign exactly r connections to each node, if each connection is bidirectional?

For example, in a 8 nodes network, have each node to have exactly 4 bidirectional connections? The closest I got for this example is 7 nodes with each 4 connections, but 1 node has 2.

My intuition tells me that there is some formula where for a number n there is a minimum r for which this is possible. In the example above, maybe n=8 nodes doesn't work for r=4, but maybe it works for n=16...

I hope my question makes sense and someone can help me here. Thanks.