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Graph Implementation – Adjacency Matrix | Set 3

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.

Adjacency Matrix
  1. adjMaxtrix[i][j] = 1 when there is edge between Vertex i and Vertex j, else 0.
  2. It’s easy to implement because removing and adding an edge takes only O(1) time.
  3. But the drawback is that it takes O(V2) space even though there are very less edges in the graph.



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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