Java Program to Find Number of Articulation Points in a Graph

This Java program is to find number of articulation points in graph. A vertex in an undirected connected graph is an articulation point (or cut vertex) iff removing it (and edges through it) disconnects the graph. Articulation points represent vulnerabilities in a connected network – single points whose failure would split the network into 2 or more disconnected components.

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

```
import java.util.HashSet;
```

import java.util.InputMismatchException;

```
import java.util.LinkedList;
```
```
import java.util.Queue;
```
```
import java.util.Scanner;
```
```
import java.util.Set;
```
```
import java.util.Stack;
```
```
 
```
```
public class NumberOfArticulationPoints
```
```
{
```
```
    private Stack<Integer> stack;
```
```
    private int numberOfNodes;
```

    private Set<Integer> articulationPoints;

```
    private int[] parent;
```
```
    private int[] visited;
```
```
    private int[][] adjacencyMatrix;
```
```
 
```

    public NumberOfArticulationPoints(int numberOfNodes)

```
    {
```

        this.numberOfNodes = numberOfNodes;

        this.stack = new Stack<Integer>();

        this.articulationPoints = new HashSet<Integer>();

        this.parent = new int[numberOfNodes + 1];

        this.visited = new int[numberOfNodes + 1];

        this.adjacencyMatrix = new int[numberOfNodes + 1][numberOfNodes + 1];

```
    }
```
```
 
```

    public int numberOfArticulationPoint(int adjacencyMatrix[][], int source)

```
    {
```
```
        int children = 0;
```
```
        int element, destination;
```
```
        stack.push(source);
```
```
        visited[source] = 1;
```
```
 
```

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

```
        {
```

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

```
            {
```

                this.adjacencyMatrix[sourceVertex][destinationVertex]

                     = adjacencyMatrix[sourceVertex][destinationVertex];

```
            }
```
```
        }
```
```
 
```
```
        while (!stack.isEmpty())
```
```
        {
```
```
            element = stack.peek();
```
```
            destination = element;
```

            while (destination <= numberOfNodes)

```
            {
```

                if (this.adjacencyMatrix[element][destination] == 1 && visited[destination] == 0)

```
                {
```

                    stack.push(destination);

                    visited[destination] = 1;

                    parent[destination] = element;

                    if (element == source)

```
                    {
```
```
                        children++;
```
```
                    }
```

                    if (!isLeaf(this.adjacencyMatrix, destination))

```
                    {
```

                        if (children > 1)

```
                        {
```

                            articulationPoints.add(source);

```
                        }
```

                        if (isArticulationPoint(this.adjacencyMatrix, destination))

```
                        {
```

                            articulationPoints.add(destination);

```
                        }
```
```
                    }
```

                    element = destination;

```
                    destination = 1;
```
```
                    continue;
```
```
                }
```
```
                destination++;
```
```
            }
```
```
            stack.pop();
```
```
        }
```

        return articulationPoints.size();

```
    }
```
```
 
```

    private boolean isArticulationPoint(int adjacencyMatrix[][], int root)

```
    {
```

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

        Stack<Integer> stack = new Stack<Integer>();

```
        stack.push(root);
```

        int element = 0, destination = 0;

```
 
```
```
        while (!stack.isEmpty())
```
```
        {
```
```
            element = stack.peek();
```
```
            destination = 1;
```

            while (destination <= numberOfNodes)

```
            {
```
```
                if ( element != root)
```
```
                {
```

                    if (adjacencyMatrix[element][destination] == 1 && visited[destination] == 1)

```
                    {
```

                        if (this.stack.contains(destination))

```
                        {
```

                            if (destination <= parent[root])

```
                            {
```

                                return false;

```
                            }
```

                            return true;

```
                        }
```
```
                    } 
```
```
                }
```

                if ((adjacencyMatrix[element][destination] == 1 && explored[destination] == 0 )

                            && visited[destination] == 0)

```
                {
```

                    stack.push(destination);

                    explored[destination] = 1;

                    adjacencyMatrix[destination][element] = 0;

                    element = destination;

```
                    destination = 1;
```
```
                    continue;
```
```
                }
```
```
                destination++;
```
```
            }
```
```
            stack.pop();
```
```
        }	
```
```
        return true;
```
```
    }
```
```
 
```

    private boolean isLeaf(int adjacencyMatrix[][], int node)

```
    {
```
```
        boolean isLeaf = true;
```

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

```
        {
```

            if (adjacencyMatrix[node][vertex] == 1 && visited[vertex] == 1)

```
            {
```
```
                 isLeaf = true;
```

            }else if (adjacencyMatrix[node][vertex] == 1 && visited[vertex] == 0)

```
            {
```
```
                 isLeaf = false;
```
```
                 break;
```
```
            }
```
```
        }
```
```
        return isLeaf;
```
```
    }
```
```
 
```

    public static void main(String... arg)

```
    {
```
```
        int number_of_nodes, source;
```
```
        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();

```
 
```

            System.out.println("Enter the source for the graph");

```
            source = scanner.nextInt();
```
```
 
```

            NumberOfArticulationPoints articulationPoints = new NumberOfArticulationPoints(number_of_nodes);

            int num = articulationPoints.numberOfArticulationPoint(adjacency_matrix, source);

            System.out.println("The number is " + num);

```
 
```

        } catch (InputMismatchException inputMismatch)

```
        {
```

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

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

$javac NumberOfArticulationPoints.java
$java NumberOfArticulationPoints
Enter the number of nodes in the graph
5
Enter the adjacency matrix
0 1 1 1 0
1 0 1 0 0
1 1 0 0 1
1 0 0 0 1
0 0 1 1 0
Enter the source for the graph
1
The Given Graph is BiConnected

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