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  "body": "\n## Summary\n\nIn graph theory, a branch of mathematics, the **modular graphs** are undirected graphs in which every three vertices $x$, $y$, and $z$ have at least one *median vertex* $m(x, y, z)$ that belongs to shortest paths between each pair of $x$, $y$, and $z$. Their name comes from the fact that a finite lattice is a modular lattice if and only if its [[Hasse diagram|00EYM7MDKS]] is a modular graph.\n",
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