---
tag: SAFDX44ZFM
kind: concept
name: Closed
sources:
  - wikipedia: en:325802@r1373839425
    locator: Glossary of graph theory, section C
    note: adopted
    mention: wikipedia://en/325802#LTSN
    sections: [Summary]
inventory: [TBA4C4FVN8]
---

## Summary

A closed neighborhood is one that includes its central vertex; see neighbourhood.

A closed walk is one that starts and ends at the same vertex; see walk.

A graph is transitively closed if it equals its own transitive closure; see transitive.

A graph property is closed under some operation on graphs if, whenever the argument or arguments to the operation have the property, then so does the result. For instance, hereditary properties are closed under induced subgraphs; monotone properties are closed under subgraphs; and minor-closed properties are closed under minors.