(definition)

**Definition:**
A *graph* whose *vertices* and *edges* are *subsets* of another *graph*.

**Formal Definition:** A *graph* G'=(V', E') is a subgraph of another graph G=(V, E) iff

- V'⊆ V, and
- E'⊆ E ∧ ( (v
_{1}, v_{2})∈ E' → v_{1}, v_{2}∈ V').

*Note:
In general, a subgraph need not have all possible edges. If a subgraph has every possible edge, it is an induced subgraph.*

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Entry modified 17 December 2004.

HTML page formatted Wed Mar 13 12:42:46 2019.

Cite this as:

Paul E. Black and Alen Lovrencic, "subgraph", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/subgraph.html