adjacency-matrix representation

(data structure)

Definition: A representation of a directed graph with n vertices using an n × n matrix, where the entry at (i,j) is 1 if there is an edge from vertex i to vertex j; otherwise the entry is 0. A weighted graph may be represented using the weight as the entry. An undirected graph may be represented using the same entry in both (i,j) and (j,i) or using an upper triangular matrix.

Aggregate parent (I am a part of or used in ...)
graph, k²-tree.

See also adjacency-list representation, dense 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
 

The adjacency-list representation is more compact for a sparse matrix, although a k²-tree can represent a sparse matrix very efficiently.

Author: SKS

Implementation

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Entry modified 8 June 2023.
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Cite this as:
Sandeep Kumar Shukla, "adjacency-matrix representation", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 8 June 2023. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/adjacencyMatrixRep.html