Program to find total number of edges in a Complete Graph

Given N number of vertices of a Graph. The task is to find the total number of edges possible in a complete graph of N vertices.
Complete Graph: A Complete Graph is a graph in which every pair of vertices is connected by an edge. 

Examples: 

Input : N = 3
Output : Edges = 3

Input : N = 5
Output : Edges = 10

The total number of possible edges in a complete graph of N vertices can be given as, 

Total number of edges in a complete graph of N vertices = ( n * ( n – 1 ) ) / 2 

Example 1: Below is a complete graph with N = 5 vertices.

The total number of edges in the above complete graph = 10 = (5)*(5-1)/2.

Implementation:

C++

// C++ implementation to find the
// number of edges in a complete graph

#include <bits/stdc++.h>
using namespace std;

// Function to find the total number of
// edges in a complete graph with N vertices
int totEdge(int n)
{
    int result = 0;

    result = (n * (n - 1)) / 2;

    return result;
}

// Driver Code
int main()
{
    int n = 6;

    cout << totEdge(n);

    return 0;
}

Java

// Java implementation to find the
// number of edges in a complete graph

class GFG {

// Function to find the total number of
// edges in a complete graph with N vertices
static int totEdge(int n)
{
    int result = 0;

    result = (n * (n - 1)) / 2;

    return result;
}

    // Driver Code
    public static void main(String []args)
    {
        int n = 6;
        System.out.println(totEdge(n));
    }

}

Python 3

# Python 3 implementation to
# find the number of edges
# in a complete graph

# Function to find the total
# number of edges in a complete
# graph with N vertices
def totEdge(n) :

    result = (n * (n - 1)) // 2

    return result

# Driver Code
if __name__ == "__main__" :

    n = 6

    print(totEdge(n))

# This code is contributed
# by ANKITRAI1

C#

// C# implementation to find
// the number of edges in a
// complete graph
using System;

class GFG
{

// Function to find the total
// number of edges in a complete
// graph with N vertices
static int totEdge(int n)
{
    int result = 0;

    result = (n * (n - 1)) / 2;

    return result;
}

// Driver Code
public static void Main()
{
    int n = 6;
    Console.Write(totEdge(n));
}
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP implementation to find
// the number of edges in a
// complete graph

// Function to find the total
// number of edges in a complete
// graph with N vertices
function totEdge($n)
{
    $result = 0;

    $result = ($n * ($n - 1)) / 2;

    return $result;
}

// Driver Code
$n = 6;
echo totEdge($n);

// This code is contributed
// by Shivi_Aggarwal
?>

Javascript

<script>

// Javascript implementation to find the
// number of edges in a complete graph

// Function to find the total number of
// edges in a complete graph with N vertices
function totEdge(n)
{
    var result = 0;

    result = (n * (n - 1)) / 2;

    return result;
}

// Driver Code
var n = 6;
document.write( totEdge(n));

</script>

Output

15

Complexity Analysis:

• Time Complexity: O(1)
• Auxiliary Space: O(1)