**graph**if and only if

(1) | $X$ is a D11: Set |

(2) | \begin{equation} \mathcal{E} \subseteq \{ E \subseteq X : |E| = 2 \} \end{equation} |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Hypergraph

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Hypergraph

Formulation 0

An D548: Ordered pair $G = (X, \mathcal{E})$ is a **graph** if and only if

(1) | $X$ is a D11: Set |

(2) | \begin{equation} \mathcal{E} \subseteq \{ E \subseteq X : |E| = 2 \} \end{equation} |

Formulation 1

An D548: Ordered pair $G = (X, \mathcal{E})$ is a **graph** if and only if

(1) | $X$ is a D11: Set |

(2) | \begin{equation} \mathcal{E} \subseteq \mathcal{P}_2(X) \end{equation} |

Also known as

Undirected graph

Child definitions