Adjacency List Representation

Last Updated : 23 Jul, 2025

An adjacency list is a data structure used to represent a graph where each node in the graph stores a list of its neighboring vertices.

Table of Content

1. Adjacency List for Directed graph:

Consider an Directed and Unweighted graph G with 3 vertices and 3 edges. For the graph G, the adjacency list would look like:

Output

Adjacency List Representation:
0: 
1: 0 2 
2: 0

Consider an Undirected and Unweighted graph G with 3 vertices and 3 edges. For the graph G, the adjacency list would look like:

Output

Adjacency List Representation:
0: 1 2 
1: 0 2 
2: 1 0

Consider an Directed and Weighted graph G with 3 vertices and 3 edges. For the graph G, the adjacency list would look like:

Output

Adjacency List Representation:
0: 
1: {0, 4} {2, 3} 
2: {0, 1}

Consider an Undirected and Weighted graph G with 3 vertices and 3 edges. For the graph G, the adjacency list would look like:

Output

Adjacency List Representation:
0: {1, 4} {2, 1} 
1: {0, 4} {2, 3} 
2: {1, 3} {0, 1}

An adjacency list representation uses a list of lists. We store all adjacent of every node together.
The size of the list is determined by the number of vertices in the graph.
All adjacent of a vertex are easily available. To find all adjacent, we need only O(n) time where is the number of adjacent vertices.

Graph algorithms: Many graph algorithms like Dijkstra's algorithm, Breadth First Search, and Depth First Search perform faster for adjacency lists to represent graphs.
Adjacency List representation is the most commonly used representation of graph as it allows easy traversal of all edges.

An adjacency list is simple and easy to understand.
Requires less space compared to adjacency matrix for sparse graphs.
Easy to traverse through all edges of a graph.
Adding an vertex is easier compared to adjacency matrix representation.
Most of the graph algorithms are implemented faster with this representation. For example, BFS and DFS implementations take OIV x V) time, but with Adjacency List representation, we get these in linear time. Similarly Prim's and Dijskstra's algorithms are implemented faster with Adjacency List representation.

Checking if there is an edge between two vertices is costly as we have traverse the adjacency list.
Not suitable for dense graphs.

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