Java Program to Find Transitive Closure of a Graph

This Java program is to find the transitive closure of a graph.Given a directed graph, find out if a vertex j is reachable from another vertex i for all vertex pairs (i, j) in the given graph. Here reachable mean that there is a path from vertex i to j. The reach-ability matrix is called transitive closure of a graph.

Here is the source code of the Java program to find the transitive closure of graph. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.Scanner;
 
public class TransitiveClosure
{
    private int transitiveMatrix[][];
    private int numberofvertices;
    public static final int INFINITY = 999;
 
    public TransitiveClosure(int numberofvertices)
    {
        transitiveMatrix= new int[numberofvertices + 1][numberofvertices + 1];
        this.numberofvertices = numberofvertices;
    }
 
    public void transitiveClosure(int adjacencymatrix[][])
    {
        for (int source = 1; source <= numberofvertices; source++)
        {
            for (int destination = 1; destination <= numberofvertices; destination++)
            {
                transitiveMatrix[destination] = adjacencymatrix[destination];
            }
        }
 
        for (int intermediate = 1; intermediate <= numberofvertices; intermediate++)
        {
            for (int source = 1; source <= numberofvertices; source++)
            {
                for (int destination = 1; destination <= numberofvertices; destination++)
                {
                    if (transitiveMatrix[intermediate] + transitiveMatrix[intermediate][destination]
                               < transitiveMatrix[destination])
                        transitiveMatrix[destination] = transitiveMatrix[intermediate] 
                                + transitiveMatrix[intermediate][destination];
                }
            }
        }
 
        for (int source = 1; source <= numberofvertices; source++)
            System.out.print("\t" + source);
 
        System.out.println();
        for (int source = 1; source <= numberofvertices; source++)
        {
            System.out.print(source + "\t");
            for (int destination = 1; destination <= numberofvertices; destination++)
            {
                System.out.print(transitiveMatrix[destination] + "\t");
            }
            System.out.println();
        }
    }
 
    public static void main(String... arg)
    {
        int adjacency_matrix[][];
        int numberofvertices;
 
        Scanner scan = new Scanner(System.in);
        System.out.println("Enter the number of vertices");
        numberofvertices = scan.nextInt();
        adjacency_matrix = new int[numberofvertices + 1][numberofvertices + 1];
 
        System.out.println("Enter the Weighted Matrix for the graph");
        for (int source = 1; source <= numberofvertices; source++)
        {
            for (int destination = 1; destination <= numberofvertices; destination++)
            {
                adjacency_matrix[destination] = scan.nextInt();
                if (source == destination)
                {
                    adjacency_matrix[destination] = 0;
                    continue;
                }
                if (adjacency_matrix[destination] == 0)
                {
                    adjacency_matrix[destination] = INFINITY;
                }
            }
        }
 
        System.out.println("The Transitive Closure of the Graph"); 
        TransitiveClosure transitiveClosure = new TransitiveClosure(numberofvertices);
        transitiveClosure.transitiveClosure(adjacency_matrix);
 
        scan.close();
    }
}

$javac TransitiveClosure.java
$java TransitiveClosure
 
Enter the number of vertices
4
 
Enter the Weighted Matrix for the graph
0 0 3 0
2 0 0 0 
0 7 0 1
6 0 0 0
 
The Transitive Closure of the Graph
 
	1	2	3	4
1	0	10	3	4	
2	2	0	5	6	
3	7	7	0	1	
4	6	16	9	0