(data structure)

**Definition:**
A representation of a *directed graph* with n *vertices* using an *array* of n *lists* of vertices. List i contains vertex j if there is an *edge* from vertex i to vertex j. A *weighted graph* may be represented with a list of vertex/weight pairs. An *undirected graph* may be represented by having vertex j in the list for vertex i and vertex i in the list for vertex j.

**See also**
*adjacency-matrix representation*, *sparse graph*.

*Note:
Suppose we have a directed graph with four vertices. Here are adjacency-matrix and adjacency-list representations. The arrow (->) means a link in a list.
*

*
*

1 2 3 4

1 1 1 1 1

2 1 0 0 0

3 0 1 0 1

4 0 1 1 0

1 -> 1 -> 2 -> 3 -> 4

2 -> 1

3 -> 2 -> 4

4 -> 2 -> 3

* One variant is to have an array of columns, rather than rows, with the list going "down". The adjacency-list representation is more compact for a sparse matrix.*

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

Entry modified 14 August 2008.

HTML page formatted Wed Mar 13 12:42:45 2019.

Cite this as:

Bob Bockholt and Paul E. Black, "adjacency-list representation", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 14 August 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/adjacencyListRep.html