I stumbled across this because I was researching what the most efficient way of implementing our FruxelGrid was. In this [StackOverflow answer](https://stackoverflow.com/a/14579347/7705525) I got pointed to graph theory.

7 Bridges of Königsberg
![[Pasted image 20231023150710.png]]
# Definitions

| Definition     | Meaning                                      |
| -------------- | -------------------------------------------- |
| Node / Vertex  | The object doing some work                   |
| Edge           | Path between two Nodes                       |
| Node degree    | Number of edges that touch the node / vertex |
| Graph          | Combination of Nodes and Vertices / Nodes    |
| Eulerian Graph | Exactly zero or two nodes have an odd degree |

# Rules
1. Exactly zero or two vertices can have an odd (=uneven) degree 

# Implementation in [[C++]]
1. **direct Translation** of the Definition: create a `std::vector` for a list of vertices and a list of edges. The edges themselves are represented as a `std::pair`
2. Adjacency List
3. Adjacency Matrix

![[Pasted image 20231023154352.png]]