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99 Work/0 OneSec/OneSecNotes/Temporary/Graph Theory.md

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+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]]