---
tag: AVM0703S4K
kind: concept
name: Modular graph
sources:
  - wikipedia: en:51807881@r1167017433
    locator: Modular graph
    note: adopted
    mention: wikipedia://en/51807881
    sections: [Summary]
same_as:
  wikidata: Q28455823
  wikipedia: Modular graph
inventory: [AMN3SFV148]
---

## Summary

In 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.