# Math & systems theory question: Nodes, links, systems

**URL:** <https://boards.straightdope.com/t/math-systems-theory-question-nodes-links-systems/815247>\
**Category:** Factual Questions\
**Created:** [June 1, 2018, 10:38am UTC](https://boards.straightdope.com/t/math-systems-theory-question-nodes-links-systems/815247 "2018-06-01T10:38:52Z")\
**Posts on this page:** 1\
**Page:** 2

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**Author:** ![rat\_avatar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rat_avatar/32/255_2.png) [@rat\_avatar](https://boards.straightdope.com/u/rat_avatar)\
**Post date:** [June 2, 2018, 8:00pm UTC](https://boards.straightdope.com/t/math-systems-theory-question-nodes-links-systems/815247/21 "2018-06-02T20:00:14Z")

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> [@Lance\_Turbo](#):
>
> As written this is incorrect. I suspect you meant to say something else or left something off.

Yes the first part should read:  
Any _vertex_ that is a member of a simple complete graph will have N-1 edges.

It is hard to be precise without a formal proof or math support, but lets most people have have good Unicode support.

In a simple complete graph you want to count how many unordered pair of vertices such pair can be exactly one edge.

Given an edge (n, υ) where n is any vertex and υ is any vertex that is not n:

```auto

             ⎛n⎞ n(n - 1)
n choose 2 = ⎜ ⎟ = ──────── 
             ⎝2⎠ 2 

```

Un-ordered pairs of edges in a simple complete graph.

But the “(n - 1)” is just the number of edges per vertex, multiplied by the number of vertexes and divided by two so that you are counting the edges and not the number of set members.

As the answer has to be a member of ℕ, or _natural numbers_, and by definition a simple complete graph. Both n and υ will have (n-1) _outgoing_ edges, or phrased in another way (n − 1) regular.

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