Java Program to Find the Edge Connectivity of a Graph

This is a java program find the edge connectivity of the given graph. The edge connectivity simply means, number of bridges in a graph, bridges are edges when removed makes the graph disconnected.

Here is the source code of the Java Program to Find the Edge Connectivity of a Graph. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

```
 
```
```
// Number of bridges in a graph
```
```
package com.sanfoundry.graph;
```
```
 
```
```
import java.util.Iterator;
```

import java.util.NoSuchElementException;

```
import java.util.Scanner;
```
```
import java.util.Stack;
```
```
 
```

class ECBag<Item> implements Iterable<Item>

```
{
```

    private int        N;    // number of elements in ECBag

    private Node<Item> first; // beginning of ECBag

```
 
```
```
    // helper linked list class
```
```
    private static class Node<Item>
```
```
    {
```
```
        private Item       item;
```
```
        private Node<Item> next;
```
```
    }
```
```
 
```
```
    public ECBag()
```
```
    {
```
```
        first = null;
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```
        N = 0;
```
```
    }
```
```
 
```
```
    public boolean isEmpty()
```
```
    {
```
```
        return first == null;
```
```
    }
```
```
 
```
```
    public int size()
```
```
    {
```
```
        return N;
```
```
    }
```
```
 
```
```
    public void add(Item item)
```
```
    {
```
```
        Node<Item> oldfirst = first;
```
```
        first = new Node<Item>();
```
```
        first.item = item;
```
```
        first.next = oldfirst;
```
```
        N++;
```
```
    }
```
```
 
```
```
    public Iterator<Item> iterator()
```
```
    {
```

        return new ListIterator<Item>(first);

```
    }
```
```
 
```

    // an iterator, doesn't implement remove() since it's optional

```
    @SuppressWarnings("hiding")
```

    private class ListIterator<Item> implements Iterator<Item>

```
    {
```
```
        private Node<Item> current;
```
```
 
```

        public ListIterator(Node<Item> first)

```
        {
```
```
            current = first;
```
```
        }
```
```
 
```
```
        public boolean hasNext()
```
```
        {
```
```
            return current != null;
```
```
        }
```
```
 
```
```
        public void remove()
```
```
        {
```

            throw new UnsupportedOperationException();

```
        }
```
```
 
```
```
        public Item next()
```
```
        {
```
```
            if (!hasNext())
```

                throw new NoSuchElementException();

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            Item item = current.item;
```
```
            current = current.next;
```
```
            return item;
```
```
        }
```
```
    }
```
```
}
```
```
 
```
```
class BridgeGraph
```
```
{
```
```
    private final int        V;
```
```
    private int              E;
```
```
    private ECBag<Integer>[] adj;
```
```
 
```
```
    @SuppressWarnings("unchecked")
```
```
    public BridgeGraph(int V)
```
```
    {
```
```
        if (V < 0)
```

            throw new IllegalArgumentException(

                    "Number of vertices must be nonnegative");

```
        this.V = V;
```
```
        this.E = 0;
```

        adj = (ECBag<Integer>[]) new ECBag[V];

```
        for (int v = 0; v < V; v++)
```
```
        {
```

            adj[v] = new ECBag<Integer>();

```
        }
```

        System.out.println("Enter the number of edges: ");

        Scanner sc = new Scanner(System.in);

```
        int E = sc.nextInt();
```
```
        if (E < 0)
```
```
        {
```
```
            sc.close();
```

            throw new IllegalArgumentException(

                    "Number of edges must be nonnegative");

```
        }
```
```
        for (int i = 0; i < E; i++)
```
```
        {
```
```
            int v = sc.nextInt();
```
```
            int w = sc.nextInt();
```
```
            addEdge(v, w);
```
```
        }
```
```
        sc.close();
```
```
    }
```
```
 
```
```
    public BridgeGraph(BridgeGraph G)
```
```
    {
```
```
        this(G.V());
```
```
        this.E = G.E();
```
```
        for (int v = 0; v < G.V(); v++)
```
```
        {
```

            // reverse so that adjacency list is in same order as original

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

```
            for (int w : G.adj[v])
```
```
            {
```
```
                reverse.push(w);
```
```
            }
```
```
            for (int w : reverse)
```
```
            {
```
```
                adj[v].add(w);
```
```
            }
```
```
        }
```
```
    }
```
```
 
```
```
    public int V()
```
```
    {
```
```
        return V;
```
```
    }
```
```
 
```
```
    public int E()
```
```
    {
```
```
        return E;
```
```
    }
```
```
 
```
```
    public void addEdge(int v, int w)
```
```
    {
```
```
        if (v < 0 || v >= V)
```

            throw new IndexOutOfBoundsException();

```
        if (w < 0 || w >= V)
```

            throw new IndexOutOfBoundsException();

```
        E++;
```
```
        adj[v].add(w);
```
```
        adj[w].add(v);
```
```
    }
```
```
 
```
```
    public Iterable<Integer> adj(int v)
```
```
    {
```
```
        if (v < 0 || v >= V)
```

            throw new IndexOutOfBoundsException();

```
        return adj[v];
```
```
    }
```
```
 
```
```
    public String toString()
```
```
    {
```

        StringBuilder s = new StringBuilder();

        String NEWLINE = System.getProperty("line.separator");

        s.append(V + " vertices, " + E + " edges " + NEWLINE);

```
        for (int v = 0; v < V; v++)
```
```
        {
```
```
            s.append(v + ": ");
```
```
            for (int w : adj[v])
```
```
            {
```
```
                s.append(w + " ");
```
```
            }
```
```
            s.append(NEWLINE);
```
```
        }
```
```
        return s.toString();
```
```
    }
```
```
}
```
```
 
```
```
public class EdgeConnectivity
```
```
{
```

    private int   bridges; // number of bridges

```
    private int   cnt;    // counter
```

    private int[] pre;    // pre[v] = order in which dfs examines v

    private int[] low;    // low[v] = lowest preorder of any vertex connected

```
                           // to v
```
```
 
```

    public EdgeConnectivity(BridgeGraph G)

```
    {
```
```
        low = new int[G.V()];
```
```
        pre = new int[G.V()];
```
```
        for (int v = 0; v < G.V(); v++)
```
```
            low[v] = -1;
```
```
        for (int v = 0; v < G.V(); v++)
```
```
            pre[v] = -1;
```
```
        for (int v = 0; v < G.V(); v++)
```
```
            if (pre[v] == -1)
```
```
                dfs(G, v, v);
```
```
    }
```
```
 
```
```
    public int components()
```
```
    {
```
```
        return bridges + 1;
```
```
    }
```
```
 
```

    private void dfs(BridgeGraph G, int u, int v)

```
    {
```
```
        pre[v] = cnt++;
```
```
        low[v] = pre[v];
```
```
        for (int w : G.adj(v))
```
```
        {
```
```
            if (pre[w] == -1)
```
```
            {
```
```
                dfs(G, v, w);
```

                low[v] = Math.min(low[v], low[w]);

```
                if (low[w] == pre[w])
```
```
                {
```

                    // System.out.println(v + "-" + w + " is a bridge");

```
                    bridges++;
```
```
                }
```
```
            }
```

            // update low number - ignore reverse of edge leading to v

```
            else if (w != u)
```

                low[v] = Math.min(low[v], pre[w]);

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

    public static void main(String[] args)

```
    {
```

        Scanner sc = new Scanner(System.in);

        System.out.println("Enter the number of vertices: ");

        BridgeGraph G = new BridgeGraph(sc.nextInt());

```
        System.out.println(G);
```

        EdgeConnectivity bridge = new EdgeConnectivity(G);

        System.out.println("Edge Connectivity: " + bridge.bridges);

```
        sc.close();
```
```
    }
```
```
}
```

Output:

$ javac EdgeConnectivity.java
$ java EdgeConnectivity
 
Enter the number of vertices: 
6
Enter the number of edges: 
7
 
0 1
1 2
1 3
3 4
4 5
5 3
5 2
6 vertices, 7 edges 
0: 1 
1: 3 2 0 
2: 5 1 
3: 5 4 1 
4: 5 3 
5: 2 3 4 
 
Edge Connectivity: 1

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