# Count single node isolated sub-graphs in a disconnected graph

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

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 <bits/stdc++.h> ` `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[7]; ` ` ` ` ` `// Representing edges ` ` ` `graph[1].push_back(2); ` ` ` `graph[2].push_back(1); ` ` ` ` ` `graph[2].push_back(3); ` ` ` `graph[3].push_back(2); ` ` ` ` ` `graph[5].push_back(6); ` ` ` `graph[6].push_back(5); ` ` ` ` ` `cout << compute(graph, N); ` `} ` |

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## 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 ` |

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## 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)) ` |

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## 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[7];
// Representing edges
graph[1] = 2;
graph[2] = 1;
graph[2] = 3;
graph[3] = 2;
graph[5] = 6;
graph[6] = 5;
Console.WriteLine(compute(graph, N));
}
}
// This code is contributed by 29AjayKumar
[tabbyending]
**Output:**

1

This article is contributed by **Rohit Thapliyal**. 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.

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