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Construct a graph from given degrees of all vertices

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  • Difficulty Level : Medium
  • Last Updated : 09 Jul, 2021

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++




// 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




// 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




# 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#




// 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

Javascript




<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 += " ";
    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>

Output:  

        (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).
 


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