Question

Consider the java Graph class below which represents an undirected graph in an adjacency list. How would you add a method to delete an edge from the graph?

// Exercise 4.1.3 (Solution published at http://algs4.cs.princeton.edu/)
package algs41;
import stdlib.*;
import algs13.Bag;

/**
* The <code>Graph</code> class represents an undirected graph of vertices
* named 0 through V-1.
* It supports the following operations: add an edge to the graph,
* iterate over all of the neighbors adjacent to a vertex.
* Parallel edges and self-loops are permitted.
* <p>
* For additional documentation, see <a href="http://algs4.cs.princeton.edu/51undirected">Section 5.1</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*/
public class Graph {
   private final int V;
   private int E;
   private final Bag<Integer>[] adj;

   /**
   * Create an empty graph with V vertices.
   */
   @SuppressWarnings("unchecked")
   public Graph(int V) {
       if (V < 0) throw new Error("Number of vertices must be nonnegative");
       this.V = V;
       this.E = 0;
       this.adj = new Bag[V];
       for (int v = 0; v < V; v++) {
           adj[v] = new Bag<>();
       }
   }
  
   /**
   * Return the number of vertices in the graph.
   */
   public int V() { return V; }

   /**
   * Return the number of edges in the graph.
   */
   public int E() { return E; }

   /**
   * Add the undirected edge v-w to graph.
   * @throws java.lang.IndexOutOfBoundsException unless both 0 <= v < V and 0 <= w < V
   */
   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);
   }

   /**
   * Return the list of neighbors of vertex v as in Iterable.
   * @throws java.lang.IndexOutOfBoundsException unless 0 <= v < V
   */
   public Iterable<Integer> adj(int v) {
       if (v < 0 || v >= V) throw new IndexOutOfBoundsException();
       return adj[v];
   }
  
    /**
     * Returns the degree of vertex {@code v}.
     *
     * @param v the vertex
     * @return the degree of vertex {@code v}
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public int degree(int v) {
       if (v < 0 || v >= V) throw new IndexOutOfBoundsException();
       return adj[v].size();
    }

   /**
   * Return a string representation of the graph.
   */
   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();
   }

   /**
   * Save a graphviz representation of the graph.
   * See <a href="http://www.graphviz.org/">graphviz.org</a>.
   */
   public void toGraphviz(String filename) {
       GraphvizBuilder gb = new GraphvizBuilder ();
       for (int v = 0; v < V; v++) {
           gb.addNode (v);
           boolean showSelfLoop = false;
           for (int w : adj[v]) {
               if (v < w) // only once each edge
                   gb.addEdge (v, w);
               if (v == w) {
                   showSelfLoop = !showSelfLoop;
                   if (showSelfLoop)
                       gb.addEdge (v, w);
               }
           }
       }
       gb.toFileUndirected (filename);
   }

   /**
   * Test client.
   */
   public static void main(String[] args) {
       //args = new String [] { "data/tinyCG.txt" };
       args = new String [] { "data/tinyG.txt" };
       //args = new String [] { "20", "40" };

       Graph G;
       if (args.length == 1) {
           In in = new In(args[0]);
           G = GraphGenerator.fromIn (in);
       } else {
           int V = Integer.parseInt (args[0]);
           int E = Integer.parseInt (args[1]);
           G = GraphGenerator.simple(V, E);
       }
       StdOut.println(G);
       G.toGraphviz ("g.png");
   }
}

Answer 1

Suppose we have to remove an edge u-v from the graph we can add the below function to the above code

public void delEdge(Vector <Integer>adj[],int u,int v)

{

for (int i = 0; i < adj[u].size(); i++)

     {

        if (adj[u].get(i) == v)

        {            

adj[u].remove(i);

            break;

        }

    }

for (int i = 0; i < adj[v].size(); i++)

    {

        if (adj[v].get(i) == u)

        {

            adj[v].remove(i);

            break;

        }

    }

}