C++ Program to Represent Graph Using Adjacency Matrix

What is Adjacency Matrix?

Adjacency matrix is a square matrix that represent a finite graph data structure using a 2D array. The each elements in the matrix represent the edges of the graph. For example, if the graph has some edges from i to j vertices, then in the adjacency matrix at i^th row and j^th column it will be 1 (or some non-zero value for weighted graph), otherwise that place will hold 0.

Graph

The image below represent a simple undirected graph with 6 vertices and 8 edges.

Adjacency Matrix

The adjacency matrix of the above graph is shown below.

Algorithm

The following are the steps to represent a graph using an adjacency matrix.

• Step 1: Start
• Step 2: Input the number of vertices V and number of edges E in the graph
• Step 3: Initialize a V x V matrix (adjMatrix) and set all values to 0.
• Step 4: For each edge, repeat step 5 to step 7.
• Step 5: Input the pair of vertices (u, v) that form an edge.
• Step 6: Set adjMatrix[u][v] = 1
• Step 7: If the graph is undirected, also set adjMatrix[v][u] = 1
• Step 8: Display the adjacency matrix.
• Step 9: End

C++ Program for Adjacency Matrix Representation of a Graph

The following C++ program demonstrates how to represent a graph using an adjacency matrix. The program allows the user to input the number of vertices and edges, and then it displays the adjacency matrix.

#include <iostream>
using namespace std;

class Graph {
private:
    int vertices;
    int **adjMatrix;
    bool isDirected;

public:
    Graph(int v, bool directed = false) {
        vertices = v;
        isDirected = directed;

        // Allocate memory for adjacency matrix
        adjMatrix = new int*[vertices];
        for (int i = 0; i < vertices; ++i) {
            adjMatrix[i] = new int[vertices];
            for (int j = 0; j < vertices; ++j) {
                adjMatrix[i][j] = 0; // Initialize with 0
            }
        }
    }

    void addEdge(int i, int j) {
        adjMatrix[i][j] = 1;
        if (!isDirected) {
            adjMatrix[j][i] = 1;
        }
    }

    void display() {
        cout << "Adjacency Matrix:\n";
        for (int i = 0; i < vertices; ++i) {
            for (int j = 0; j < vertices; ++j) {
                cout << adjMatrix[i][j] << " ";
            }
            cout << endl;
        }
    }

    ~Graph() {
        for (int i = 0; i < vertices; ++i) {
            delete[] adjMatrix[i];
        }
        delete[] adjMatrix;
    }
};

int main() {
    int V, E;
    cout << "Enter number of vertices: ";
    cin >> V;

    Graph g(V);  // Change to Graph g(V, true); for directed graph

    cout << "Enter number of edges: ";
    cin >> E;

    cout << "Enter edges (format: from to):\n";
    for (int i = 0; i < E; ++i) {
        int from, to;
        cin >> from >> to;
        g.addEdge(from, to);
    }

    g.display();

    return 0;
}

Sample Output

The output of the above program is as follows: