**graph**if and only if

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

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

Definition D778

Graph

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} |

Children

▶ | Complete graph |

▶ | Digraph-generated graph |

▶ | Graph complement |

▶ | Graph homomorphism |

▶ | Graph intersection |

▶ | Graph tensor product |

▶ | Graph union |

▶ | Subgraph |