This is a java program to generate a random graph using number of edges provided by user. 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 Generate a Random UnDirected Graph for a Given Number of Edges. 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 undirected graph where numbers of edges is given by user`

import java.util.HashMap;

import java.util.LinkedList;

import java.util.List;

import java.util.Map;

import java.util.Random;

import java.util.Scanner;

public class Random_Undirected_Graph

`{`

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

public Random_Undirected_Graph(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("Enter the number of edges: ");

Scanner sc = new Scanner(System.in);

int e = sc.nextInt();

`try`

`{`

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

int maxV = e + 1;

Random random = new Random();

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

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

Random_Undirected_Graph rug = new Random_Undirected_Graph(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);

rug.setEdge(to, from);

`count++;`

`}`

System.out

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

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

`{`

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

List<Integer> edgeList = rug.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");

`}`

sc.close();

`}`

`}`

Output:

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$ javac Random_Undirected_Graph.java $ java Random_Undirected_Graph Enter the number of edges: 15 Random graph has 6 vertices The Adjacency List Representation of the graph is: 1 -> 4 -> 2 -> 3 -> 5 2 -> 2 -> 2 -> 1 -> 5 3 -> 5 -> 6 -> 4 -> 6 -> 1 -> 5 -> 4 4 -> 6 -> 4 -> 4 -> 1 -> 3 -> 3 5 -> 3 -> 6 -> 3 -> 1 -> 2 6 -> 4 -> 3 -> 5 -> 3

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