Construct a graph from given degrees of all vertices

This is a C++ program to generate a graph for a given fixed degree sequence. This algorithm generates a undirected graph for the given degree sequence.It does not include self-edge and multiple edges.

Examples: 

Input : degrees[] = {2, 2, 1, 1}
Output :  (0)  (1)  (2)  (3)
    (0)    0    1    1    0                              
    (1)    1    0    0    1                   
    (2)    1    0    0    0                       
    (3)    0    1    0    0     
Explanation : We are given that there
are four vertices with degree of vertex
0 as 2, degree of vertex 1 as 2, degree
of vertex 2 as 1 and degree of vertex 3
as 1. Following is graph that follows
given conditions.                   
    (0)----------(1)
     |            | 
     |            | 
     |            |
    (2)          (3) 

Approach : 

1. Take the input of the number of vertexes and their corresponding degree. 
2. Declare adjacency matrix, mat[ ][ ] to store the graph. 
3. To create the graph, create the first loop to connect each vertex ‘i’. 
4. Second nested loop to connect the vertex ‘i’ to the every valid vertex ‘j’, next to it. 
5. If the degree of vertex ‘i’ and ‘j’ are more than zero then connect them. 
6. Print the adjacency matrix.

Based on the above explanation, below are implementations:

// C++ program to generate a graph for a
// given fixed degrees
#include <bits/stdc++.h>
using namespace std;

// A function to print the adjacency matrix.
void printMat(int degseq[], int n)
{
    // n is number of vertices
    int mat[n][n];
    memset(mat, 0, sizeof(mat));

    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {

            // For each pair of vertex decrement
            // the degree of both vertex.
            if (degseq[i] > 0 && degseq[j] > 0) {
                degseq[i]--;
                degseq[j]--;
                mat[i][j] = 1;
                mat[j][i] = 1;
            }
        }
    }

    // Print the result in specified format
    cout << "\n"
         << setw(3) << "     ";
    for (int i = 0; i < n; i++)
        cout << setw(3) << "(" << i << ")";
    cout << "\n\n";
    for (int i = 0; i < n; i++) {
        cout << setw(4) << "(" << i << ")";
        for (int j = 0; j < n; j++)
            cout << setw(5) << mat[i][j];
        cout << "\n";
    }
}

// driver program to test above function
int main()
{
    int degseq[] = { 2, 2, 1, 1, 1 };
    int n = sizeof(degseq) / sizeof(degseq[0]);
    printMat(degseq, n);
    return 0;
}

// Java program to generate a graph for a
// given fixed degrees
import java.util.*;

class GFG
{

// A function to print the adjacency matrix.
static void printMat(int degseq[], int n)
{
    // n is number of vertices
    int [][]mat = new int[n][n];

    for (int i = 0; i < n; i++) 
    {
        for (int j = i + 1; j < n; j++)
        {

            // For each pair of vertex decrement
            // the degree of both vertex.
            if (degseq[i] > 0 && degseq[j] > 0) 
            {
                degseq[i]--;
                degseq[j]--;
                mat[i][j] = 1;
                mat[j][i] = 1;
            }
        }
    }

    // Print the result in specified format
    System.out.print("\n" + setw(3) + "     ");
    
    for (int i = 0; i < n; i++)
        System.out.print(setw(3) + "(" + i + ")");
    System.out.print("\n\n");
    for (int i = 0; i < n; i++)
    {
        System.out.print(setw(4) + "(" + i + ")");
        
        for (int j = 0; j < n; j++)
            System.out.print(setw(5) + mat[i][j]);
        System.out.print("\n");
    }
}

static String setw(int n)
{
    String space = "";
    while(n-- > 0)
        space += " ";
    return space;
}

// Driver Code
public static void main(String[] args)
{
    int degseq[] = { 2, 2, 1, 1, 1 };
    int n = degseq.length;
    printMat(degseq, n);
}
}

// This code is contributed by 29AjayKumar

# Python3 program to generate a graph 
# for a given fixed degrees 

# A function to print the adjacency matrix. 
def printMat(degseq, n):
    
    # n is number of vertices 
    mat = [[0] * n for i in range(n)]

    for i in range(n):
        for j in range(i + 1, n):

            # For each pair of vertex decrement 
            # the degree of both vertex. 
            if (degseq[i] > 0 and degseq[j] > 0):
                degseq[i] -= 1
                degseq[j] -= 1
                mat[i][j] = 1
                mat[j][i] = 1

    # Print the result in specified form
    print("      ", end = " ")
    for i in range(n):
        print(" ", "(", i, ")", end = "") 
    print()
    print()
    for i in range(n):
        print(" ", "(", i, ")", end = "")
        for j in range(n):
            print("     ", mat[i][j], end = "") 
        print()

# Driver Code
if __name__ == '__main__': 
    degseq = [2, 2, 1, 1, 1] 
    n = len(degseq)
    printMat(degseq, n)

# This code is contributed by PranchalK

// C# program to generate a graph for a
// given fixed degrees
using System;
    
class GFG
{

// A function to print the adjacency matrix.
static void printMat(int []degseq, int n)
{
    // n is number of vertices
    int [,]mat = new int[n, n];

    for (int i = 0; i < n; i++) 
    {
        for (int j = i + 1; j < n; j++)
        {

            // For each pair of vertex decrement
            // the degree of both vertex.
            if (degseq[i] > 0 && degseq[j] > 0) 
            {
                degseq[i]--;
                degseq[j]--;
                mat[i, j] = 1;
                mat[j, i] = 1;
            }
        }
    }

    // Print the result in specified format
    Console.Write("\n" + setw(3) + "     ");
    
    for (int i = 0; i < n; i++)
        Console.Write(setw(3) + "(" + i + ")");
    Console.Write("\n\n");
    for (int i = 0; i < n; i++)
    {
        Console.Write(setw(4) + "(" + i + ")");
        
        for (int j = 0; j < n; j++)
            Console.Write(setw(5) + mat[i, j]);
        Console.Write("\n");
    }
}

static String setw(int n)
{
    String space = "";
    while(n-- > 0)
        space += " ";
    return space;
}

// Driver Code
public static void Main(String[] args)
{
    int []degseq = { 2, 2, 1, 1, 1 };
    int n = degseq.Length;
    printMat(degseq, n);
}
}

// This code is contributed by Princi Singh

<script>

// JavaScript program to generate a graph for a
// given fixed degrees

// A function to print the adjacency matrix.
function printMat(degseq,n)
{
    // n is number of vertices
    let mat = new Array(n);
    for(let i=0;i<n;i++)
    {
        mat[i]=new Array(n);
        for(let j=0;j<n;j++)
            mat[i][j]=0;
    }
  
    for (let i = 0; i < n; i++) 
    {
        for (let j = i + 1; j < n; j++)
        {
  
            // For each pair of vertex decrement
            // the degree of both vertex.
            if (degseq[i] > 0 && degseq[j] > 0) 
            {
                degseq[i]--;
                degseq[j]--;
                mat[i][j] = 1;
                mat[j][i] = 1;
            }
        }
    }
  
    // Print the result in specified format
    document.write("<br>" + setw(3) + "     ");
      
    for (let i = 0; i < n; i++)
        document.write(setw(3) + "(" + i + ")");
    document.write("<br><br>");
    for (let i = 0; i < n; i++)
    {
        document.write(setw(4) + "(" + i + ")");
          
        for (let j = 0; j < n; j++)
            document.write(setw(5) + mat[i][j]);
        document.write("<br>");
    }
}

function setw(n)
{
    let space = "";
    while(n-- > 0)
        space += "&nbsp";
    return space;
}

// Driver Code
let degseq=[2, 2, 1, 1, 1];
let n = degseq.length;
printMat(degseq, n);

// This code is contributed by rag2127

</script>

       (0)  (1)  (2)  (3)  (4)

   (0)    0    1    1    0    0
   (1)    1    0    0    1    0
   (2)    1    0    0    0    0
   (3)    0    1    0    0    0
   (4)    0    0    0    0    0

Time Complexity: O(v*v).

Space complexity : O(n^2) because it creates a 2-dimensional array (matrix) of size n * n, where n is the number of vertices in the graph.