This is a java program to generate a random graph by selecting random number of edges. One important thing to note here is, that we need to decide minimum and maximum number of nodes such that all edges get accommodated. Minimum number of vertices is positive solution to n(n-1) = 2e, where e is number of edges and maximum number of vertices is e+1.

Here is the source code of the Java Program to Construct a Random Graph by the Method of Random Edge Selection. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to randomly generate a graph using random edge selection`

import java.util.HashMap;

import java.util.LinkedList;

import java.util.List;

import java.util.Map;

import java.util.Random;

public class Random_Edges_Graph2

`{`

private Map<Integer, List<Integer>> adjacencyList;

public Random_Edges_Graph2(int v)

`{`

adjacencyList = new HashMap<Integer, List<Integer>>();

for (int i = 1; i <= v; i++)

adjacencyList.put(i, new LinkedList<Integer>());

`}`

public void setEdge(int to, int from)

`{`

if (to > adjacencyList.size() || from > adjacencyList.size())

System.out.println("The vertices does not exists");

List<Integer> sls = adjacencyList.get(to);

sls.add(from);

List<Integer> dls = adjacencyList.get(from);

dls.add(to);

`}`

public List<Integer> getEdge(int to)

`{`

if (to > adjacencyList.size())

`{`

System.out.println("The vertices does not exists");

return null;

`}`

return adjacencyList.get(to);

`}`

public static void main(String args[])

`{`

System.out.println("Random Graph Generation");

Random random = new Random();

int e = Math.abs(random.nextInt(21 - 1) + 1);

`try`

`{`

int minV = (int) Math.ceil((1 + Math.sqrt(1 + 8 * e)) / 2);

int maxV = e + 1;

int v = Math.abs(random.nextInt(maxV - minV) + minV);

System.out.println("Random graph has "+v+" vertices");

System.out.println("Random graph has "+e+" edges");

Random_Edges_Graph2 reg = new Random_Edges_Graph2(v);

int count = 1, to, from;

while (count <= e)

`{`

to = Math.abs(random.nextInt(v + 1 - 1) + 1);

from = Math.abs(random.nextInt(v + 1 - 1) + 1);

reg.setEdge(to, from);

`count++;`

`}`

System.out

.println("The Adjacency List Representation of the random graph is: ");

for (int i = 1; i <= v; i++)

`{`

System.out.print(i + " -> ");

List<Integer> edgeList = reg.getEdge(i);

if (edgeList.size() == 0)

System.out.print("null");

`else`

`{`

for (int j = 1;; j++)

`{`

if (j != edgeList.size())

System.out.print(edgeList.get(j - 1) + " -> ");

else {

System.out.print(edgeList.get(j - 1));

break;

`}`

`}`

`}`

System.out.println();

`}`

`}`

catch (Exception E)

`{`

System.out.println("Something went wrong");

`}`

`}`

`}`

Output:

$ javac Random_Edges_Graph2.java $ java Random_Edges_Graph2 Random Graph Generation Random graph has 4 vertices Random graph has 5 edges The Adjacency List Representation of the random graph is: 1 -> 4 2 -> 3 -> 3 -> 4 3 -> 3 -> 3 -> 2 -> 2 4 -> 1 -> 2

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