# 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.

Below is the implementation of the above idea:

## 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; ` `} ` |

*chevron_right*

*filter_none*

## 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)); ` ` ` `} ` ` ` `} ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

15

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: **DSA Self Paced**. Become industry ready at a student-friendly price.

## Recommended Posts:

- Ways to Remove Edges from a Complete Graph to make Odd Edges
- Program to find the diameter, cycles and edges of a Wheel Graph
- Maximum number of edges that N-vertex graph can have such that graph is Triangle free | Mantel's Theorem
- Count number of edges in an undirected graph
- Minimum number of edges between two vertices of a graph using DFS
- Maximum number of edges in Bipartite graph
- Minimum number of edges between two vertices of a Graph
- Number of Simple Graph with N Vertices and M Edges
- Maximum number of edges among all connected components of an undirected graph
- Maximum number of edges to be added to a tree so that it stays a Bipartite graph
- Find weight of MST in a complete graph with edge-weights either 0 or 1
- Program to find the number of region in Planar Graph
- Total number of Spanning Trees in a Graph
- Total number of Spanning trees in a Cycle Graph
- Total number of days taken to complete the task if after certain days one person leaves
- Program to find the time remaining for the day to complete
- All vertex pairs connected with exactly k edges in a graph
- Path with minimum XOR sum of edges in a directed graph
- Shortest path with exactly k edges in a directed and weighted graph
- Largest subset of Graph vertices with edges of 2 or more colors

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.