(definition)

**Definition:**
A *graph* in which the number of *edges* is much less than the possible number of edges.

**Generalization** (I am a kind of ...)

*graph*.

**See also**
*dense graph*, *complete graph*, *adjacency-list representation*.

*Note:
A directed graph can have at most n(n-1) edges, where n is the number of vertices. An undirected graph can have at most n(n-1)/2 edges. *

* There is no strict distinction between sparse and dense graphs. Bruno Preiss' definition of sparse and dense graphs has problems, but may help. First, for one graph, one can always choose a k. Second a class of graphs might be considered sparse if |E| = O(|V| ^{k}) and 1 < k < 2. |E| is the number of edges, and |V| is the number of vertices. Preiss reference from Andreas Leiser <andreas.leiser@bluewin.ch> 22 December 2003*

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 14 August 2008.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "sparse graph", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 14 August 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/sparsegraph.html