Convert Adjacency List to Adjacency Matrix representation of a Graph

Given an adjacency list representation of a Graph, the task is to convert the given Adjacency List to Adjacency Matrix representation.

Examples:

Input: adjList[] = {{0 –> 1 –> 3}, {1 –> 2}, {2 –> 3}}
Output:
0 1 0 1
0 0 1 0
0 0 0 1
0 0 0 0

Input: adjList[] = {{0 –> 1 –> 4}, {1 –> 0 –> 2 –> 3 –> 4}, {2 –> 1 –> 3}, {3 –> 1 –> 2 –> 4}, {4 –> 0 –> 1 –> 3}}
Output:
0 1 0 0 1
1 0 1 1 1
0 1 0 1 0
0 1 1 0 1
1 1 0 1 0

Adjacency List: An array of lists is used. The size of the array is equal to the number of vertices. Let the array be an array[]. An entry array[i] represents the list of vertices adjacent to the ith Vertex.



Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j.

Follow the steps below to convert an adjacency list to an adjacency matrix:

  • Initialize a matrix with 0s.
  • Iterate over the vertices in the adjacency list
  • For every jth vertex in the adjacency list, traverse its edges.
  • For each vertex i with which the jth vertex has an edge, set mat[i][j] = 1.

Below is the implementation of the above approach:

C++

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// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to insert vertices to adjacency list
void insert(vector<int> adj[], int u, int v)
{
    // Insert a vertex v to vertex u
    adj[u].push_back(v);
    return;
}
  
// Function to display adjacency list
void printList(vector<int> adj[], int V)
{
    for (int i = 0; i < V; i++) {
        cout << i;
        for (auto j : adj[i])
            cout << " --> " << j;
        cout << endl;
    }
    cout << endl;
}
  
// Function to convert adjacency
// list to adjacency matrix
vector<vector<int> > convert(vector<int> adj[],
                             int V)
{
    // Initialize a matrix
    vector<vector<int> > matrix(V,
                                vector<int>(V, 0));
  
    for (int i = 0; i < V; i++) {
        for (auto j : adj[i])
            matrix[i][j] = 1;
    }
    return matrix;
}
  
// Function to display adjacency matrix
void printMatrix(vector<vector<int> > adj, int V)
{
    for (int i = 0; i < V; i++) {
        for (int j = 0; j < V; j++) {
            cout << adj[i][j] << "   ";
        }
        cout << endl;
    }
    cout << endl;
}
  
// Driver code
int main()
{
    int V = 5;
  
    vector<int> adjList[V];
  
    // Inserting edges
    insert(adjList, 0, 1);
    insert(adjList, 0, 4);
    insert(adjList, 1, 0);
    insert(adjList, 1, 2);
    insert(adjList, 1, 3);
    insert(adjList, 1, 4);
    insert(adjList, 2, 1);
    insert(adjList, 2, 3);
    insert(adjList, 3, 1);
    insert(adjList, 3, 2);
    insert(adjList, 3, 4);
    insert(adjList, 4, 0);
    insert(adjList, 4, 1);
    insert(adjList, 4, 3);
  
    // Display adjacency list
    cout << "Adjacency List: \n";
    printList(adjList, V);
  
    // Function call which returns
    // adjacency matrix after conversion
    vector<vector<int> > adjMatrix
        = convert(adjList, V);
  
    // Display adjacency matrix
    cout << "Adjacency Matrix: \n";
    printMatrix(adjMatrix, V);
  
    return 0;
}

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Output:

Adjacency List: 
0 --> 1 --> 4
1 --> 0 --> 2 --> 3 --> 4
2 --> 1 --> 3
3 --> 1 --> 2 --> 4
4 --> 0 --> 1 --> 3

Adjacency Matrix: 
0   1   0   0   1   
1   0   1   1   1   
0   1   0   1   0   
0   1   1   0   1   
1   1   0   1   0

Time Complexity: O(N*M)
Auxiliary Space: O(N2)

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