---
tag: 6NCN51F7AE
kind: concept
name: Twin
sources:
  - wikipedia: en:325802@r1373839425
    locator: Glossary of graph theory, section T
    note: adopted
    mention: wikipedia://en/325802#DGPI
    sections: [Summary]
inventory: [Y051NHCDS4]
---

## Summary

Two vertices $u,v$ are true twins if they have the same closed neighborhood: $N_{G}[u] = N_{G}[v]$ (this implies $u$ and $v$ are neighbors), and they are false twins if they have the same open neighborhood: $N_{G}(u) = N_{G}(v))$ (this implies $u$ and $v$ are not neighbors).