# Count of distinct graphs that can be formed with N vertices

Given an integer N which is the number of vertices. The task is to find the number of distinct graphs that can be formed. Since the answer can be very large, print the answer % 1000000007.

Examples:

Input: N = 3
Output: 8

Input: N = 4
Output: 64

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

Approach:

• The maximum number of edges a graph with N vertices can contain is X = N * (N – 1) / 2.
• The total number of graphs containing 0 edge and N vertices will be XC0
• The total number of graphs containing 1 edge and N vertices will be XC1
• And so on from number of edges 1 to X with N vertices
• Hence, the total number of graphs that can be formed with n vertices will be:
XC0 + XC1 + XC2 + … + XCX = 2X.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `MOD = 1e9 + 7; ` ` `  `// Function to return (x^y) % MOD ` `// in O(log(y)) ` `long` `long` `power(``long` `long` `x, ` `                ``long` `long` `y, ` `                ``const` `int``& MOD) ` `{ ` `    ``long` `long` `res = 1; ` `    ``while` `(y > 0) { ` `        ``if` `(y & 1) ` `            ``res = (res * x) % MOD; ` `        ``x = (x * x) % MOD; ` `        ``y /= 2; ` `    ``} ` `    ``return` `res; ` `} ` ` `  `// Function to return the count of distinct ` `// graphs possible with n vertices ` `long` `long` `countGraphs(``int` `n) ` `{ ` ` `  `    ``// Maximum number of edges for a ` `    ``// graph with n vertices ` `    ``long` `long` `x = n * (n - 1) / 2; ` ` `  `    ``// Function to calculate ` `    ``// (2^x) % mod ` `    ``return` `power(2, x, MOD); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` ` `  `    ``cout << countGraphs(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG  ` `{ ` `    ``static` `final` `int` `MOD = (``int``)1e9 + ``7``;  ` `     `  `    ``// Function to return (x^y) % MOD  ` `    ``// in O(log(y))  ` `    ``static` `long` `power(``long` `x,  ` `                      ``long` `y) ` `    ``{  ` `        ``long` `res = ``1``;  ` `        ``while` `(y > ``0``)  ` `        ``{  ` `            ``if` `((y & ``1``) != ``0``)  ` `                ``res = (res * x) % MOD;  ` `            ``x = (x * x) % MOD;  ` `            ``y /= ``2``;  ` `        ``}  ` `        ``return` `res;  ` `    ``}  ` `     `  `    ``// Function to return the count of distinct  ` `    ``// graphs possible with n vertices  ` `    ``static` `long` `countGraphs(``int` `n)  ` `    ``{  ` `     `  `        ``// Maximum number of edges for a  ` `        ``// graph with n vertices  ` `        ``long` `x = n * (n - ``1``) / ``2``;  ` `     `  `        ``// Function to calculate  ` `        ``// (2^x) % mod  ` `        ``return` `power(``2``, x);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{  ` `        ``int` `n = ``5``;  ` `     `  `        ``System.out.println(countGraphs(n));  ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python

 `MOD ``=` `int``(``1e9` `+` `7``) ` ` `  `# Function to return the count of distinct ` `# graphs possible with n vertices ` `def` `countGraphs(n): ` ` `  `    ``# Maximum number of edges for a ` `    ``# graph with n vertices ` `    ``x ``=` `(n ``*``( n ``-` `1` `)) ``/``/``2` `     `  `    ``# Return 2 ^ x ` `    ``return` `(``pow``(``2``, x, MOD)) ` ` `  `# Driver code ` `n ``=` `5` `print``(countGraphs(n)) `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``static` `int` `MOD = (``int``)1e9 + 7;  ` `     `  `    ``// Function to return (x^y) % MOD  ` `    ``// in O(log(y))  ` `    ``static` `long` `power(``long` `x, ``long` `y) ` `    ``{  ` `        ``long` `res = 1;  ` `        ``while` `(y > 0)  ` `        ``{  ` `            ``if` `((y & 1) != 0)  ` `                ``res = (res * x) % MOD;  ` `            ``x = (x * x) % MOD;  ` `            ``y /= 2;  ` `        ``}  ` `        ``return` `res;  ` `    ``}  ` `     `  `    ``// Function to return the count of distinct  ` `    ``// graphs possible with n vertices  ` `    ``static` `long` `countGraphs(``int` `n)  ` `    ``{  ` `     `  `        ``// Maximum number of edges for a  ` `        ``// graph with n vertices  ` `        ``long` `x = n * (n - 1) / 2;  ` `     `  `        ``// Function to calculate  ` `        ``// (2^x) % mod  ` `        ``return` `power(2, x);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `n = 5;  ` `     `  `        ``Console.Write(countGraphs(n));  ` `    ``} ` `} ` ` `  `// This code is contributed by ajit. `

Output:

```1024
```

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Improved By : AnkitRai01, jit_t