Earlier we had discussed in Graph Representation – Adjacency Matrix and Adjacency List about Graph and its different representations and we read Graph Implementation – Adjacency List .In this article we will implement graph using adjacency matrix.

We would recommend to read the theory part of Graph Representation – Adjacency Matrix and Adjacency List before continue reading this article.

Let’s revise few basic concepts:

**What is Graph:**

*G = (V,E)*

Graph is a collection of nodes or vertices (V) and edges(E) between them. We can traverse these nodes using the edges. These edges might be weighted or non-weighted.

**Adjacency Matrix:**

Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. See the example below, the Adjacency matrix for the graph shown above.

- adjMaxtrix[i][j] = 1 when there is edge between Vertex i and Vertex j, else 0.
- It’s easy to implement because removing and adding an edge takes only O(1) time.
- But the drawback is that it takes O(V
^{2}) space even though there are very less edges in the graph.

*Complete Code for Graph Using Adjacency Matrix:*

**Output:**

Graph: (Adjacency Matrix)
0 1 0 0 1
1 0 1 1 1
0 1 0 1 0
0 1 1 0 1
1 1 0 1 0
Vertex 0 is connected to:1 4
Vertex 1 is connected to:0 2 3 4
Vertex 2 is connected to:1 3
Vertex 3 is connected to:1 2 4
Vertex 4 is connected to:0 1 3

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.

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