Java Program to Check whether a Graph is Bipartite using 2 Color Algorithm

This Java program is to Check whether Graph is a Bipartite using 2 Color Algorithm.In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets and such that every edge connects a vertex in to one in ; that is, and are each independent sets.
The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in green, each edge has endpoints of differing colors, as is required in the graph coloring problem.In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle.

Here is the source code of the Java program to Check whether Graph is a Bipartite using 2 Color Algorithm. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.InputMismatchException;

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import java.util.Scanner;
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public class CheckBipartite
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{
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    private int numberOfNodes;
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    private static final int NO_OF_COLOR = 2;

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    private boolean isSafe(int vertex,int[][] adjacencyMatrix, int [] colored, int color)

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    {
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        for (int destination = 1; destination <= numberOfNodes; destination++)

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        {
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            if (adjacencyMatrix[vertex][destination] == 1 && colored[destination] == color)

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            {
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                return false;
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            }
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        }
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        return true;
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    }
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    private boolean checkBipartiteUtil(int adjacencyMatrix[][], int[] colored, int vertex)

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    {
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        if (vertex > numberOfNodes)
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        {
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            return true;
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        }
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        for (int colorNum = 1; colorNum <= NO_OF_COLOR; colorNum++)

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        {
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            if (isSafe(vertex, adjacencyMatrix, colored, colorNum))

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            {
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                colored[vertex] = colorNum;

                if (checkBipartiteUtil(adjacencyMatrix, colored, vertex + 1))

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                {  
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                    return true;
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                }
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                else
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                {
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                    return false;
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                }
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            }	
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        }
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        return false;
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    }
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    public boolean checkBipartite(int adjacencyMatrix[][])

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    {
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        boolean bipartite = true;
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        numberOfNodes = adjacencyMatrix[1].length - 1;

        int[] colored = new int[numberOfNodes + 1];

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        for (int vertex = 1; vertex <= numberOfNodes; vertex++)

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        {
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            colored[vertex] = 0;
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        }
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        if (!checkBipartiteUtil(adjacencyMatrix, colored, 1))

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        {
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            bipartite = false;
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        }
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        return bipartite;
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    }
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```
 
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    public static void main(String... arg)

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    {
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        int number_of_nodes;
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        Scanner scanner = null;
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        try
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        {
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            System.out.println("Enter the number of nodes in the graph");

            scanner = new Scanner(System.in);

            number_of_nodes = scanner.nextInt();

```
 
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            int adjacency_matrix[][] = new int[number_of_nodes + 1][number_of_nodes + 1];

            System.out.println("Enter the adjacency matrix");

            for (int i = 1; i <= number_of_nodes; i++)

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            {
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                for (int j = 1; j <= number_of_nodes; j++)

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                {	
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                    adjacency_matrix[i][j] = scanner.nextInt();

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                }
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            }
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            for (int i = 1; i <= number_of_nodes; i++)

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            {
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                for (int j = 1; j <= number_of_nodes; j++)

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                {	
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                    if (adjacency_matrix[i][j] == 1 && adjacency_matrix[j][i] == 0)

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                    {
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                        adjacency_matrix[j][i] = 1;

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                    }
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                }
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            }			
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            CheckBipartite bipartite = new CheckBipartite();

            if (bipartite.checkBipartite(adjacency_matrix))

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            {
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                System.out.println("the given graph is bipartite");

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            }
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            else
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            {
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                System.out.println("the given graph is not bipartite");

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            }
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        }
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        catch (InputMismatchException inputMismatch)

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        {
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            System.out.println("Wrong Input format");

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        }
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        scanner.close();
```
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    }	
```
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}
```

$javac CheckBipartite.java
$java CheckBipartite
 
Enter the number of nodes in the graph
6
Enter the adjacency matrix
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 0 1 0 1 0
the given graph is bipartite