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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
Edge



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)

    handshaking 

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 uhown 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;
}

Python3

# Python3 program to count number of 
# edge in undirected graph 
  
# Adjacency list representation of graph 
class Graph:
    def __init__(self, V):
        self.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 uhown 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


Output:

14

Time Complexity: O(V)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

tags:

Graph Graph

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