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  "body": "\n## Definition\n\nA graph, or simple graph, is a pair $G = (V, E)$ of a set $V$ and a set $E$ of $2$-element subsets of $V$.\nThe elements of $V$ are the vertices of $G$, and the elements of $E$ are its edges.\nTwo vertices $u$ and $v$ are adjacent if $\\{u, v\\} \\in E$. The notation for this edge is $uv$, and the notation for adjacency is $u \\sim v$.\n\nEquivalently, a graph is a set $V$ with a relation $\\sim$ on $V$ that is symmetric and irreflexive.\nA graph is finite if $V$ is finite.\n\n## Remarks\n\nIn a simple graph, no edge joins a vertex to itself, and two vertices are joined by at most one edge. A [[multigraph|01M5T0KDG7]] drops the second condition, and some variants allow loops.\nIn a [[directed graph|0R5HTV7REV]] the edges are ordered pairs.\nThe set $E$ is the [[edge set|0WNGQBPPQX]] of $G$.\n\n## Explanations\n\n### L1 human\n\nA graph is a set of points with lines between some pairs of points.\nFor example, the people at a party are vertices, and two people are joined by an edge when they know each other.\n",
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