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Program to find total number of edges in a Complete Graph
• Difficulty Level : Basic
• Last Updated : 22 Oct, 2018

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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.

Below is the implementation of the above idea:

## C++

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

 ` `

Output:

```15
```

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