Java Program to Find Strongly Connected Components in Graphs

This Java program, displays the Strong Connected Components of graph.A directed graph is called strongly connected if there is a path from each vertex in the graph to every other vertex. In particular , this means paths in each direction; a path from a to b and also a path from b to a.

Here is the source code of the Java program to display the Strong Connected Components of a graph. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.Scanner;
import java.util.Stack;
  
public class StrongConnectedComponents
{
    private int leader = 0;
    private int[] leader_node;
    private int explore[];
    private int finishing_time_of_node[];
    private int finishing_time = 1;
    private int number_of_nodes;
    private Stack<Integer> stack;
    private Map<Integer, Integer> finishing_time_map;
  
    public StrongConnectedComponents(int number_of_nodes)
    {
        this.number_of_nodes = number_of_nodes;
        leader_node = new int[number_of_nodes + 1];
        explore = new int[number_of_nodes + 1];
        finishing_time_of_node = new int[number_of_nodes + 1];
        stack = new Stack<Integer>();
        finishing_time_map = new HashMap<Integer, Integer>();
    }
  
    public void strongConnectedComponent(int adjacency_matrix[][])
    {
        for (int i = number_of_nodes; i > 0; i--)
        {
            if (explore[i] == 0)
            {
                dfs_1(adjacency_matrix, i);
            }
        }
        int rev_matrix[][] = new int[number_of_nodes + 1][number_of_nodes + 1];
        for (int i = 1; i <= number_of_nodes; i++)
        {
            for (int j = 1; j <= number_of_nodes; j++)
            {
                if (adjacency_matrix[i][j] == 1)
                    rev_matrix[finishing_time_of_node[j]][finishing_time_of_node[i]] = adjacency_matrix[i][j];
            }
        }
  
        for (int i = 1; i <= number_of_nodes; i++)
        {
            explore[i] = 0;
            leader_node[i] = 0;
        }
  
        for (int i = number_of_nodes; i > 0; i--)
        {
            if (explore[i] == 0)
            {
                leader = i;
                dfs_2(rev_matrix, i);
            }
        }
    }
  
    public void dfs_1(int adjacency_matrix[][], int source)
    {
        explore = 1;
        stack.push(source);
        int i = 1;
        int element = source;
  
        while (!stack.isEmpty())
        {
            element = stack.peek();
            i = 1;
            while (i <= number_of_nodes)
            {
                if (adjacency_matrix[element][i] == 1 && explore[i] == 0)
                {
                    stack.push(i);
                    explore[i] = 1;
                    element = i;
                    i = 1;
                    continue;
                }
                i++;
            }
            int poped = stack.pop();
            int time = finishing_time++;
            finishing_time_of_node[poped] = time;
            finishing_time_map.put(time, poped);
        }
    }
  
    public void dfs_2(int rev_matrix[][], int source)
    {
        explore = 1;
        leader_node[finishing_time_map.get(source)] = leader;
        stack.push(source);
        int i = 1;
        int element = source;
        while (!stack.isEmpty())
        {
            element = stack.peek();
            i = 1;
            while (i <= number_of_nodes)
            {
                if (rev_matrix[element][i] == 1 && explore[i] == 0)
                {
                    if (leader_node[finishing_time_map.get(i)] == 0)
                        leader_node[finishing_time_map.get(i)] = leader;
                    stack.push(i);
                    explore[i] = 1;
                    element = i;
                    i = 1;
                    continue;
                }
                i++;
            }
            stack.pop();
        }
    }
  
    public static void main(String... arg)
    { 
        int number_of_nodes;
        Scanner scanner = null;
        try
        {
            System.out.println("Enter the number of nodes in the graph");
            scanner = new Scanner(System.in);
            number_of_nodes = scanner.nextInt();
  
            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++)
                for (int j = 1; j <= number_of_nodes; j++)   
                    adjacency_matrix[i][j] = scanner.nextInt();
  
            StrongConnectedComponents strong = new StrongConnectedComponents(number_of_nodes);
            strong.strongConnectedComponent(adjacency_matrix);
  
            System.out.println("The Strong Connected Components are");
            for (int i = 1; i < strong.leader_node.length; i++)
            {
                System.out.println( "Node " + i+ "belongs to SCC"
                    + strong.finishing_time_map.get(strong.leader_node[i]));
            }
        } catch (InputMismatchException inputMismatch)
        {   
            System.out.println("Wrong Input Format");
        }
    }
}

$javac StrongConnectedComponents.java
$java StrongConnectedComponenets
Enter the number of nodes in the graph
8
Enter the adjacency matrix
0 1 0 0 0 0 0 0
0 0 0 0 0 0 1 0
0 0 0 1 1 0 0 0
0 1 0 0 0 0 1 0
0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0
0 0 0 0 0 1 0 0
0 0 1 1 0 0 0 0
The Strong Connected Components are
Node 1 belongs to SCC 2
Node 2 belongs to SCC 2
Node 3 belongs to SCC 8
Node 4 belongs to SCC 4
Node 5 belongs to SCC 8
Node 6 belongs to SCC 2
Node 7 belongs to SCC 2
Node 8 belongs to SCC 8