Java Program to Check Whether a Graph is Bipartite using BFS

This Java program is to check whether graph is bipartite using bfs. 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. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.

Here is the source code of the Java program to check whether a graph is biparite using bfs. 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.LinkedList;
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import java.util.Queue;
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import java.util.Scanner;
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public class BipartiteBfs
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{
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    private int numberOfVertices;
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    private Queue<Integer> queue;
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    public static final int NO_COLOR = 0;

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    public static final int RED = 1;
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    public static final int BLUE = 2;
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    public BipartiteBfs(int numberOfVertices)

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    {
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        this.numberOfVertices = numberOfVertices;

        queue = new LinkedList<Integer>();

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    }
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    public boolean isBipartite(int adjacencyMatrix[][], int source)

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    {
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        int[] colored = new int[numberOfVertices +  1];

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

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        {
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            colored[vertex] = NO_COLOR;
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        }
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        colored[source] = RED;
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        queue.add(source);
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        int element, neighbour;
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        while (!queue.isEmpty())
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        {
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            element = queue.remove();
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            neighbour = 1;
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            while (neighbour <= numberOfVertices)

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            { 
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                if (adjacencyMatrix[element][neighbour] == 1 && colored[element]== colored[neighbour])

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                {
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                    return false;
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                }
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                if (adjacencyMatrix[element][neighbour] == 1 && colored[neighbour]== NO_COLOR)

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                {
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                    colored[neighbour] = (colored[element] == RED ) ? BLUE :RED;

                    queue.add(neighbour);

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                }
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                neighbour++;
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            }
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        }
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        return true;
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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, source;
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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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           System.out.println("Enter the source for the graph");

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           source = scanner.nextInt();
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           BipartiteBfs bipartiteBfs = new BipartiteBfs(number_of_nodes);

           if (bipartiteBfs.isBipartite(adjacency_matrix, source))

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

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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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       } 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 BipartiteBfs.java
$java BipartiteBfs
Enter the number of nodes in the graph
4
Enter the adjacency matrix
0 1 0 1
1 0 1 0
0 1 0 1
1 0 1 0
Enter the source for the graph
1
The given graph is bipartite