Finding in and out degrees of all vertices in a graph

Last Updated : 13 Feb, 2023

Given a directed graph, the task is to count the in and out degree of each vertex of the graph.

Examples:

Input:

Output:
Vertex    In    Out
0         1    2
1          2    1
2          2    3
3          2    2
4          2    2
5          2    2
6          2    1

Approach: Traverse adjacency list for every vertex, if size of the adjacency list of vertex i is x then the out degree for i = x and increment the in degree of every vertex that has an incoming edge from i. Repeat the steps for every vertex and print the in and out degrees for all the vertices in the end.

Below is the implementation of the above approach:

C++

// C++ program to find the in and out degrees
// of the vertices of the given graph
#include <bits/stdc++.h>
using namespace std;

// Function to print the in and out degrees
// of all the vertices of the given graph
void findInOutDegree(vector<vector<int>> adjlist,
                     int n)
{
    vector<int> iN(n,0);
      vector<int> ouT(n,0);

    
    
    for(int i=0;i<n;i++)
    {
        // Out degree for ith vertex will be the count
        // of direct paths from i to other vertices
       ouT[i] = adjlist[i].size();
          // Every vertex that has an incoming
            // edge from i
           for(int j=0;j<adjlist[i].size();j++)
          iN[adjlist[i][j]]++;
     }

    cout << "Vertex\t\tIn\t\tOut" << endl;
    for(int k = 0; k < n; k++)
    {
        cout << k << "\t\t"
             << iN[k] << "\t\t" 
             << ouT[k] << endl;
    }
}

// Driver code
int main()
{
    
    // Adjacency list representation of the graph
    vector<vector<int>> adjlist;

    // Vertices 1 and 2 have an incoming edge
    // from vertex 0
    vector<int> tmp;
    tmp.push_back(1);
    tmp.push_back(2);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertex 3 has an incoming edge 
    // from vertex 1
    tmp.push_back(3);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertices 0, 5 and 6 have an incoming
    // edge from vertex 2
    tmp.push_back(0);
    tmp.push_back(5);
    tmp.push_back(6);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertices 1 and 4 have an incoming 
    // edge from vertex 3
    tmp.push_back(1);
    tmp.push_back(4);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertices 2 and 3 have an incoming 
    // edge from vertex 4
    tmp.push_back(2);
    tmp.push_back(3);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertices 4 and 6 have an incoming 
    // edge from vertex 5
    tmp.push_back(4);
    tmp.push_back(6);
    adjlist.push_back(tmp);
    tmp.clear();

    // Vertex 5 has an incoming 
    // edge from vertex 6
    tmp.push_back(5);
    adjlist.push_back(tmp);
    tmp.clear();

    int n = adjlist.size();
    
    findInOutDegree(adjlist, n);
}

// This code is contributed by saurabhgpta248

Java

// Java program to find the in and out degrees
// of the vertices of the given graph
import java.util.*;

class GFG {

    // Function to print the in and out degrees
    // of all the vertices of the given graph
    static void findInOutDegree(List<List<Integer> > adjList, int n)
    {
        int in[] = new int[n];
        int out[] = new int[n];

        for (int i = 0; i < adjList.size(); i++) {

            List<Integer> list = adjList.get(i);

            // Out degree for ith vertex will be the count
            // of direct paths from i to other vertices
            out[i] = list.size();
            for (int j = 0; j < list.size(); j++)

                // Every vertex that has an incoming 
                // edge from i
                in[list.get(j)]++;
        }

        System.out.println("Vertex\tIn\tOut");
        for (int k = 0; k < n; k++) {
            System.out.println(k + "\t" + in[k] + "\t" + out[k]);
        }
    }

    // Driver code
    public static void main(String args[])
    {
        // Adjacency list representation of the graph
        List<List<Integer> > adjList = new ArrayList<>();

        // Vertices 1 and 2 have an incoming edge 
        // from vertex 0
        List<Integer> tmp = 
           new ArrayList<Integer>(Arrays.asList(1, 2));
        adjList.add(tmp);

        // Vertex 3 has an incoming edge from vertex 1
        tmp = new ArrayList<Integer>(Arrays.asList(3));
        adjList.add(tmp);

        // Vertices 0, 5 and 6 have an incoming
        // edge from vertex 2
        tmp = 
          new ArrayList<Integer>(Arrays.asList(0, 5, 6));
        adjList.add(tmp);

        // Vertices 1 and 4 have an incoming edge 
        // from vertex 3
        tmp = new ArrayList<Integer>(Arrays.asList(1, 4));
        adjList.add(tmp);

        // Vertices 2 and 3 have an incoming edge
        // from vertex 4
        tmp = new ArrayList<Integer>(Arrays.asList(2, 3));
        adjList.add(tmp);

        // Vertices 4 and 6 have an incoming edge
        // from vertex 5
        tmp = new ArrayList<Integer>(Arrays.asList(4, 6));
        adjList.add(tmp);

        // Vertex 5 has an incoming edge from vertex 6
        tmp = new ArrayList<Integer>(Arrays.asList(5));
        adjList.add(tmp);

        int n = adjList.size();
        findInOutDegree(adjList, n);
    }
}

Python3

# Python3 program to find the in and out 
# degrees of the vertices of the given graph 

# Function to print the in and out degrees 
# of all the vertices of the given graph 
def findInOutDegree(adjList, n): 
    
    _in = [0] * n 
    out = [0] * n

    for i in range(0, len(adjList)): 

        List = adjList[i] 

        # Out degree for ith vertex will be the count 
        # of direct paths from i to other vertices 
        out[i] = len(List) 
        for j in range(0, len(List)): 

            # Every vertex that has 
            # an incoming edge from i 
            _in[List[j]] += 1

    print("Vertex\tIn\tOut") 
    for k in range(0, n): 
        print(str(k) + "\t" + str(_in[k]) + 
                       "\t" + str(out[k])) 

# Driver code 
if __name__ == "__main__": 
    
    # Adjacency list representation of the graph 
    adjList = [] 

    # Vertices 1 and 2 have an incoming edge 
    # from vertex 0 
    adjList.append([1, 2]) 

    # Vertex 3 has an incoming edge from vertex 1 
    adjList.append([3]) 

    # Vertices 0, 5 and 6 have an 
    # incoming edge from vertex 2 
    adjList.append([0, 5, 6]) 

    # Vertices 1 and 4 have an 
    # incoming edge from vertex 3 
    adjList.append([1, 4]) 

    # Vertices 2 and 3 have an 
    # incoming edge from vertex 4 
    adjList.append([2, 3]) 

    # Vertices 4 and 6 have an 
    # incoming edge from vertex 5 
    adjList.append([4, 6]) 

    # Vertex 5 has an incoming edge from vertex 6 
    adjList.append([5]) 

    n = len(adjList) 
    findInOutDegree(adjList, n) 
    
# This code is contributed by Rituraj Jain

// C# program to find the in and out degrees
// of the vertices of the given graph
using System;
using System.Collections.Generic;    

class GFG
{

// Function to print the in and out degrees
// of all the vertices of the given graph
static void findInOutDegree(List<List<int>> adjList, int n)
{
    int []iN = new int[n];
    int []ouT = new int[n];

    for (int i = 0; i < adjList.Count; i++) 
    {

        List<int> list = adjList[i];

        // Out degree for ith vertex will be the count
        // of direct paths from i to other vertices
        ouT[i] = list.Count;
        for (int j = 0; j < list.Count; j++)

            // Every vertex that has an incoming 
            // edge from i
            iN[list[j]]++;
    }

    Console.WriteLine("Vertex\t\tIn\t\tOut");
    for (int k = 0; k < n; k++)
    {
        Console.WriteLine(k + "\t\t" + 
                      iN[k] + "\t\t" + ouT[k]);
    }
}

// Driver code
public static void Main(String []args)
{
    // Adjacency list representation of the graph
    List<List<int> > adjList = new List<List<int>>();

    // Vertices 1 and 2 have an incoming edge 
    // from vertex 0
    List<int> tmp = 
    new List<int>{1, 2};
    adjList.Add(tmp);

    // Vertex 3 has an incoming edge from vertex 1
    tmp = new List<int>{3};
    adjList.Add(tmp);

    // Vertices 0, 5 and 6 have an incoming
    // edge from vertex 2
    tmp = 
    new List<int>{0, 5, 6};
    adjList.Add(tmp);

    // Vertices 1 and 4 have an incoming edge 
    // from vertex 3
    tmp = new List<int>{1, 4};
    adjList.Add(tmp);

    // Vertices 2 and 3 have an incoming edge
    // from vertex 4
    tmp = new List<int>{2, 3};
    adjList.Add(tmp);

    // Vertices 4 and 6 have an incoming edge
    // from vertex 5
    tmp = new List<int>{4, 6};
    adjList.Add(tmp);

    // Vertex 5 has an incoming edge from vertex 6
    tmp = new List<int>{5};
    adjList.Add(tmp);

    int n = adjList.Count;
    findInOutDegree(adjList, n);
}
}

// This code is contributed by 29AjayKumar

JavaScript

// JavaScript program to find the in and out 
// degrees of the vertices of the given graph 

// Function to print the in and out degrees 
// of all the vertices of the given graph 
function findInOutDegree(adjList, n) { 

    // Initialize arrays to store in-degree 
    // and out-degree of all vertices
    let inDegree = Array(n).fill(0);
    let outDegree = Array(n).fill(0);

    // Loop through each vertex in the graph
    for (let i = 0; i < adjList.length; i++) { 

        // Get the list of vertices that are 
        //connected to the current vertex
        let list = adjList[i]; 

        // Out-degree for the current vertex 
        // will be the count of direct paths 
        // from the current vertex to other vertices 
        outDegree[i] = list.length;

        // Loop through each vertex that 
        // is connected to the current vertex
        for (let j = 0; j < list.length; j++) { 

            // Increase the in-degree for the vertex 
            // that has an incoming edge from the current vertex
            inDegree[list[j]] += 1;
        }
    }

    // Print the in-degree and out-degree of all vertices
    document.write("Vertex   In    Out"+"<br>");
    for (let k = 0; k < n; k++) { 
        document.write(k + "   " + inDegree[k] + "   " + outDegree[k]+"<br>"); 
    }
}

// Driver code 

    
    // Adjacency list representation of the graph 
    let adjList = []; 

    // Vertices 1 and 2 have an incoming edge from vertex 0 
    adjList.push([1, 2]); 

    // Vertex 3 has an incoming edge from vertex 1 
    adjList.push([3]); 

    // Vertices 0, 5, and 6 have an incoming edge from vertex 2 
    adjList.push([0, 5, 6]); 

    // Vertices 1 and 4 have an incoming edge from vertex 3 
    adjList.push([1, 4]); 

    // Vertices 2 and 3 have an incoming edge from vertex 4 
    adjList.push([2, 3]); 

    // Vertices 4 and 6 have an incoming edge from vertex 5 
    adjList.push([4, 6]); 

    // Vertex 5 has an incoming edge from vertex 6 
    adjList.push([5]); 

    // Number of vertices in the graph
    let n = adjList.length; 

    // Call the findInOutDegree function to 
    // find and print the in-degree and out-degree of all vertices
    findInOutDegree(adjList, n);

Output

Vertex        In        Out
0        1        2
1        2        1
2        2        3
3        2        2
4        2        2
5        2        2
6        2        1

Complexity Analysis:

Time Complexity: O(V + E) where V and E are the numbers of vertices and edges in the graph respectively.
Auxiliary Space: O(V + E).

Construct a graph from given degrees of all vertices

janice_shah

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Finding in and out degrees of all vertices in a graph

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