 (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.

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

Algorithms and Data Structures' implementation (Java and C++). Sedgewick and Wayne "Algorithms" 4th edition's implementation (Java).