# Count number of edges in an undirected graph

Given an adjacency list representation undirected graph. Write a function to count the number of edges in the undirected graph.

Expected time complexity : O(V)

**Examples:**

Input : Adjacency list representation of below graph. Output : 9

Idea is based on Handshaking Lemma. Handshaking lemma is about undirected graph. In every finite undirected graph number of vertices with odd degree is always even. The handshaking lemma is a consequence of the degree sum formula (also sometimes called the handshaking lemma)

So we traverse all vertices, compute sum of sizes of their adjacency lists, and finally returns sum/2. Below implementation of above idea

## C++

`// C++ program to count number of edge in` `// undirected graph` `#include<bits/stdc++.h>` `using` `namespace` `std;` ` ` `// Adjacency list representation of graph` `class` `Graph` `{` ` ` `int` `V ;` ` ` `list < ` `int` `> *adj;` `public` `:` ` ` `Graph( ` `int` `V )` ` ` `{` ` ` `this` `->V = V ;` ` ` `adj = ` `new` `list<` `int` `>[V];` ` ` `}` ` ` `void` `addEdge ( ` `int` `u, ` `int` `v ) ;` ` ` `int` `countEdges () ;` `};` ` ` `// add edge to graph` `void` `Graph :: addEdge ( ` `int` `u, ` `int` `v )` `{` ` ` `adj[u].push_back(v);` ` ` `adj[v].push_back(u);` `}` ` ` `// Returns count of edge in undirected graph` `int` `Graph :: countEdges()` `{` ` ` `int` `sum = 0;` ` ` ` ` `//traverse all vertex` ` ` `for` `(` `int` `i = 0 ; i < V ; i++)` ` ` ` ` `// add all edge that are linked to the` ` ` `// current vertex` ` ` `sum += adj[i].size();` ` ` ` ` ` ` `// The count of edge is always even because in` ` ` `// undirected graph every edge is connected` ` ` `// twice between two vertices` ` ` `return` `sum/2;` `}` ` ` `// driver program to check above function` `int` `main()` `{` ` ` `int` `V = 9 ;` ` ` `Graph g(V);` ` ` ` ` `// making above shown graph` ` ` `g.addEdge(0, 1 );` ` ` `g.addEdge(0, 7 );` ` ` `g.addEdge(1, 2 );` ` ` `g.addEdge(1, 7 );` ` ` `g.addEdge(2, 3 );` ` ` `g.addEdge(2, 8 );` ` ` `g.addEdge(2, 5 );` ` ` `g.addEdge(3, 4 );` ` ` `g.addEdge(3, 5 );` ` ` `g.addEdge(4, 5 );` ` ` `g.addEdge(5, 6 );` ` ` `g.addEdge(6, 7 );` ` ` `g.addEdge(6, 8 );` ` ` `g.addEdge(7, 8 );` ` ` ` ` `cout << g.countEdges() << endl;` ` ` ` ` `return` `0;` `}` |

## Java

`// Java program to count number of edge in ` `// undirected graph` `import` `java.io.*;` `import` `java.util.*;` ` ` `// Adjacency list representation of graph` `class` `Graph ` `{` ` ` `int` `V;` ` ` `Vector<Integer>[] adj;` ` ` ` ` `//@SuppressWarnings("unchecked")` ` ` `Graph(` `int` `V)` ` ` `{` ` ` `this` `.V = V;` ` ` `this` `.adj = ` `new` `Vector[V];` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < V; i++)` ` ` `adj[i] = ` `new` `Vector<Integer>();` ` ` `}` ` ` ` ` `// add edge to graph` ` ` `void` `addEdge(` `int` `u, ` `int` `v)` ` ` `{` ` ` `adj[u].add(v);` ` ` `adj[v].add(u);` ` ` `}` ` ` ` ` `// Returns count of edge in undirected graph` ` ` `int` `countEdges()` ` ` `{` ` ` `int` `sum = ` `0` `;` ` ` ` ` `// traverse all vertex` ` ` `for` `(` `int` `i = ` `0` `; i < V; i++)` ` ` ` ` `// add all edge that are linked to the` ` ` `// current vertex` ` ` `sum += adj[i].size();` ` ` ` ` `// The count of edge is always even because in` ` ` `// undirected graph every edge is connected` ` ` `// twice between two vertices` ` ` `return` `sum / ` `2` `;` ` ` `}` `}` ` ` `class` `GFG ` `{` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args) ` `throws` `IOException ` ` ` `{` ` ` `int` `V = ` `9` `;` ` ` `Graph g = ` `new` `Graph(V);` ` ` ` ` `// making above shown graph` ` ` `g.addEdge(` `0` `, ` `1` `);` ` ` `g.addEdge(` `0` `, ` `7` `);` ` ` `g.addEdge(` `1` `, ` `2` `);` ` ` `g.addEdge(` `1` `, ` `7` `);` ` ` `g.addEdge(` `2` `, ` `3` `);` ` ` `g.addEdge(` `2` `, ` `8` `);` ` ` `g.addEdge(` `2` `, ` `5` `);` ` ` `g.addEdge(` `3` `, ` `4` `);` ` ` `g.addEdge(` `3` `, ` `5` `);` ` ` `g.addEdge(` `4` `, ` `5` `);` ` ` `g.addEdge(` `5` `, ` `6` `);` ` ` `g.addEdge(` `6` `, ` `7` `);` ` ` `g.addEdge(` `6` `, ` `8` `);` ` ` `g.addEdge(` `7` `, ` `8` `);` ` ` ` ` `System.out.println(g.countEdges());` ` ` `}` `}` ` ` `// This code is contributed by` `// sanjeev2552` |

## Python3

`# Python3 program to count number of ` `# edge in undirected graph ` ` ` `# Adjacency list representation of graph ` `class` `Graph:` ` ` `def` `__init__(` `self` `, V):` ` ` `self` `.V ` `=` `V ` ` ` `self` `.adj ` `=` `[[] ` `for` `i ` `in` `range` `(V)]` ` ` ` ` `# add edge to graph ` ` ` `def` `addEdge (` `self` `, u, v ):` ` ` `self` `.adj[u].append(v) ` ` ` `self` `.adj[v].append(u)` ` ` ` ` `# Returns count of edge in undirected graph ` ` ` `def` `countEdges(` `self` `):` ` ` `Sum` `=` `0` ` ` ` ` `# traverse all vertex ` ` ` `for` `i ` `in` `range` `(` `self` `.V):` ` ` ` ` `# add all edge that are linked ` ` ` `# to the current vertex ` ` ` `Sum` `+` `=` `len` `(` `self` `.adj[i]) ` ` ` ` ` `# The count of edge is always even ` ` ` `# because in undirected graph every edge ` ` ` `# is connected twice between two vertices ` ` ` `return` `Sum` `/` `/` `2` ` ` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `V ` `=` `9` ` ` `g ` `=` `Graph(V) ` ` ` ` ` `# making above shown graph ` ` ` `g.addEdge(` `0` `, ` `1` `) ` ` ` `g.addEdge(` `0` `, ` `7` `) ` ` ` `g.addEdge(` `1` `, ` `2` `) ` ` ` `g.addEdge(` `1` `, ` `7` `) ` ` ` `g.addEdge(` `2` `, ` `3` `) ` ` ` `g.addEdge(` `2` `, ` `8` `) ` ` ` `g.addEdge(` `2` `, ` `5` `) ` ` ` `g.addEdge(` `3` `, ` `4` `) ` ` ` `g.addEdge(` `3` `, ` `5` `) ` ` ` `g.addEdge(` `4` `, ` `5` `) ` ` ` `g.addEdge(` `5` `, ` `6` `) ` ` ` `g.addEdge(` `6` `, ` `7` `) ` ` ` `g.addEdge(` `6` `, ` `8` `) ` ` ` `g.addEdge(` `7` `, ` `8` `) ` ` ` ` ` `print` `(g.countEdges())` ` ` `# This code is contributed by PranchalK` |

## C#

`// C# program to count number of edge in ` `// undirected graph` `using` `System;` `using` `System.Collections.Generic;` ` ` `// Adjacency list representation of graph` `class` `Graph ` `{` ` ` `public` `int` `V;` ` ` `public` `List<` `int` `>[] adj;` ` ` `public` `Graph(` `int` `V)` ` ` `{` ` ` `this` `.V = V;` ` ` `this` `.adj = ` `new` `List<` `int` `>[V];` ` ` ` ` `for` `(` `int` `i = 0; i < V; i++)` ` ` `adj[i] = ` `new` `List<` `int` `>();` ` ` `}` ` ` ` ` `// add edge to graph` ` ` `public` `void` `addEdge(` `int` `u, ` `int` `v)` ` ` `{` ` ` `adj[u].Add(v);` ` ` `adj[v].Add(u);` ` ` `}` ` ` ` ` `// Returns count of edge in undirected graph` ` ` `public` `int` `countEdges()` ` ` `{` ` ` `int` `sum = 0;` ` ` ` ` `// traverse all vertex` ` ` `for` `(` `int` `i = 0; i < V; i++)` ` ` ` ` `// add all edge that are linked to the` ` ` `// current vertex` ` ` `sum += adj[i].Count;` ` ` ` ` `// The count of edge is always even because in` ` ` `// undirected graph every edge is connected` ` ` `// twice between two vertices` ` ` `return` `sum / 2;` ` ` `}` `}` ` ` `class` `GFG ` `{` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `int` `V = 9;` ` ` `Graph g = ` `new` `Graph(V);` ` ` ` ` `// making above shown graph` ` ` `g.addEdge(0, 1);` ` ` `g.addEdge(0, 7);` ` ` `g.addEdge(1, 2);` ` ` `g.addEdge(1, 7);` ` ` `g.addEdge(2, 3);` ` ` `g.addEdge(2, 8);` ` ` `g.addEdge(2, 5);` ` ` `g.addEdge(3, 4);` ` ` `g.addEdge(3, 5);` ` ` `g.addEdge(4, 5);` ` ` `g.addEdge(5, 6);` ` ` `g.addEdge(6, 7);` ` ` `g.addEdge(6, 8);` ` ` `g.addEdge(7, 8);` ` ` ` ` `Console.WriteLine(g.countEdges());` ` ` `}` `}` ` ` `// This code is contributed by PrinciRaj1992` |

**Output:**

14

**Time Complexity:** O(V)

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