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Count single node isolated sub-graphs in a disconnected graph
• Difficulty Level : Basic
• Last Updated : 16 Sep, 2019

A disconnected Graph with N vertices and K edges is given. The task is to find the count of singleton sub-graphs. A singleton graph is one with only single vertex.

Examples:

```Input :
Vertices : 6
Edges :    1 2
1 3
5 6
Output : 1
Explanation :  The Graph has 3 components : {1-2-3}, {5-6}, {4}
Out of these, the only component forming singleton graph is {4}.
```

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

The idea is simple for graph given as adjacency list representation. We traverse the list and find the indices(representing a node) with no elements in list, i.e. no connected components.

Below is the representation :

## C++

 `// CPP code to count the singleton sub-graphs``// in a disconnected graph``#include ``using` `namespace` `std;`` ` `// Function to compute the count``int` `compute(vector<``int``> graph[], ``int` `N)``{``    ``// Storing intermediate result``    ``int` `count = 0;`` ` `    ``// Traversing the Nodes``    ``for` `(``int` `i = 1; i <= N; i++)`` ` `        ``// Singleton component``        ``if` `(graph[i].size() == 0)``            ``count++;    `` ` `    ``// Returning the result``    ``return` `count;``}`` ` `// Driver``int` `main()``{``    ``// Number of nodes``    ``int` `N = 6;`` ` `    ``// Adjacency list for edges 1..6``    ``vector<``int``> graph;`` ` `    ``// Representing edges``    ``graph.push_back(2);``    ``graph.push_back(1);`` ` `    ``graph.push_back(3);``    ``graph.push_back(2);`` ` `    ``graph.push_back(6);``    ``graph.push_back(5);`` ` `    ``cout << compute(graph, N);``}`

## Java

 `// Java code to count the singleton sub-graphs ``// in a disconnected graph ``import` `java.util.*;`` ` `class` `GFG``{`` ` `// Function to compute the count ``static` `int` `compute(``int` `[]graph, ``int` `N) ``{ ``    ``// Storing intermediate result ``    ``int` `count = ``0``; ``     ` `    ``// Traversing the Nodes ``    ``for` `(``int` `i = ``1``; i < ``7``; i++) ``    ``{``        ``// Singleton component ``        ``if` `(graph[i] == ``0``) ``            ``count++;     ``    ``}``         ` `    ``// Returning the result ``    ``return` `count; ``} `` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Number of nodes ``    ``int` `N = ``6``; `` ` `    ``// Adjacency list for edges 1..6 ``    ``int` `[]graph = ``new` `int``[``7``];``    ``// Representing edges ``    ``graph[``1``] = ``2``;``    ``graph[``2``] = ``1``;``    ``graph[``2``] = ``3``;``    ``graph[``3``] = ``2``;``    ``graph[``5``] = ``6``;``    ``graph[``6``] = ``5``;`` ` `    ``System.out.println(compute(graph, N)); ``}``}`` ` `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python code to count the singleton sub-graphs ``# in a disconnected graph ``  ` `# Function to compute the count ``def` `compute(graph, N):``    ``# Storing intermediate result ``    ``count ``=` `0` `   ` `    ``# Traversing the Nodes``    ``for` `i ``in` `range``(``1``, N``+``1``):``   ` `        ``# Singleton component ``        ``if` `(``len``(graph[i]) ``=``=` `0``):``            ``count ``+``=` `1`    `   ` `    ``# Returning the result ``    ``return` `count``   ` `# Driver ``if` `__name__ ``=``=` `'__main__'``:`` ` `    ``# Number of nodes ``    ``N ``=` `6` `   ` `    ``# Adjacency list for edges 1..6 ``    ``graph ``=` `[[] ``for` `i ``in` `range``(``7``)] ``   ` `    ``# Representing edges ``    ``graph[``1``].append(``2``) ``    ``graph[``2``].append(``1``) ``   ` `    ``graph[``2``].append(``3``) ``    ``graph[``3``].append(``2``) ``   ` `    ``graph[``5``].append(``6``) ``    ``graph[``6``].append(``5``) ``   ` `    ``print``(compute(graph, N))`

## C#

 `// C# code to count the singleton sub-graphs ``// in a disconnected graph ``using` `System;`` ` `class` `GFG``{`` ` `// Function to compute the count ``static` `int` `compute(``int` `[]graph, ``int` `N) ``{ ``    ``// Storing intermediate result ``    ``int` `count = 0; ``     ` `    ``// Traversing the Nodes ``    ``for` `(``int` `i = 1; i < 7; i++) ``    ``{``        ``// Singleton component ``        ``if` `(graph[i] == 0) ``            ``count++;     ``    ``}``         ` `    ``// Returning the result ``    ``return` `count; ``} `` ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``// Number of nodes ``    ``int` `N = 6; `` ` `    ``// Adjacency list for edges 1..6 ``    ``int` `[]graph = ``new` `int``;``     ` `    ``// Representing edges ``    ``graph = 2;``    ``graph = 1;``    ``graph = 3;``    ``graph = 2;``    ``graph = 6;``    ``graph = 5;`` ` `    ``Console.WriteLine(compute(graph, N)); ``}``}`` ` `// This code is contributed by 29AjayKumar`

Output:

```1
```

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