Adjacency list representation, Data Structure & Algorithms

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Adjacency list representation

An Adjacency list representation of Graph G = {V, E} contains an array of adjacency lists mentioned by adj of V list. For each of the vertex u?V, adj[u] contains all vertices adjacent to u in the graph G.

Consider the graph of Figure.

636_Adjacency list representation.png

Figure: A Graph

Given is the adjacency list representation of graph of above Figure:

adj [1] = {2, 3, 5}

adj [2] = {1, 4}

adj [3] = {1, 4, 5}

adj [4] = {2, 3, 5}

 adj [5] = {1, 3, 4}

An adjacency matrix representation of a Graph G=(V, E) is a matrix

The adjacency matrix for the graph of Figure is following:

 

1

2

3

4

5

1

0

1

1

0

1

 

2

 

1

 

0

 

0

 

1

 

1

 

3

 

1

 

0

 

0

 

1

 

1

 

4

 

0

 

1

 

1

 

0

 

1

 

5

 

1

 

0

 

1

 

1

 

0

 

 

 

 

 

 

Observe that the matrix is symmetric along the main diagonal. If we described the adjacency matrix as A and the transpose as AT , then for undirected graph G as above, A = AT.


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