===== Undirected graph =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $V,E$ ... set |
| @#FFBB00: definiendum | @#FFBB00: $ \langle V,\langle E,\psi\rangle\rangle \in \mathrm{it}(E,V) $ |
| @#55EE55: postulate   | @#55EE55: $ \psi $ ... function |
| @#55EE55: postulate   | @#55EE55: $ \mathrm{dom}(\psi)=E $ |
| @#55EE55: postulate   | @#55EE55: $ \forall (e\in E).\ \exists (u,v\in V).\ \psi(e) = \{v,u\} $ |

==== Discussion ====
In the above definition, the set $E=\{a,b,\dots\}$ in $\langle E,\psi\rangle$ is any set whos elements then each label an edge, e.g. $\psi(a)=\{v,w\}$. 

Instead, one can also define a graph using a [[multiset]] $\langle E_\mathrm{ends},m\rangle$ where $E_\mathrm{ends}=\{\{v,w\},\{u,w\},\dots\}$ is itself a set of endpoints and $m:E_\mathrm{ends}\to\mathbb N$ counts the number of instances such a pair is part of the graph. The definitions are of course practically equivalent, the definition above with $\psi$ de-emphasises the focus on "$v$ and $w$ from $V$ are things which are connected" in favor of "$a$ is something from $E$ which connects the things $v$ and $w$ from $V$".
==== Parents ====
=== Subset of ===
[[Graph]]
=== Context ===
[[Function]]