How to Implement Adjacency Matrix in C: Simple Guide

To implement an adjacency matrix in C, create a 2D array where each cell matrix[i][j] represents the presence (1) or absence (0) of an edge between nodes i and j. Initialize the matrix with zeros and update it to 1 where edges exist.

Syntax

An adjacency matrix in C is a 2D array of integers. Each row and column represents a node in the graph. The value at matrix[i][j] is 1 if there is an edge from node i to node j, otherwise 0.

You declare it as int matrix[size][size]; where size is the number of nodes.

c

int matrix[size][size];

Example

This example shows how to create a graph with 4 nodes and add edges between them using an adjacency matrix. It prints the matrix to show connections.

c

#include <stdio.h>

#define SIZE 4

int main() {
    int matrix[SIZE][SIZE] = {0}; // Initialize all to 0

    // Add edges: 0->1, 0->2, 1->2, 2->3
    matrix[0][1] = 1;
    matrix[0][2] = 1;
    matrix[1][2] = 1;
    matrix[2][3] = 1;

    // Print adjacency matrix
    printf("Adjacency Matrix:\n");
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            printf("%d ", matrix[i][j]);
        }
        printf("\n");
    }

    return 0;
}

Output

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

Common Pitfalls

• Forgetting to initialize the matrix to zero can cause garbage values, leading to wrong edges.
• Mixing up row and column indices will create incorrect edges.
• Not matching the matrix size to the number of nodes causes out-of-bounds errors.

c

#include <stdio.h>

#define SIZE 3

int main() {
    int matrix[SIZE][SIZE]; // Not initialized

    // Wrong: adding edge with swapped indices
    matrix[1][0] = 1; // Edge from 1 to 0

    // Printing without initialization may show garbage
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            printf("%d ", matrix[i][j]);
        }
        printf("\n");
    }

    return 0;
}

// Correct way: initialize with zeros and use matrix[i][j] properly.

Quick Reference

• Declare: int matrix[size][size];
• Initialize: Set all elements to 0 before adding edges.
• Add edge: matrix[from][to] = 1;
• Check edge: if(matrix[i][j] == 1) means edge exists.

Key Takeaways

An adjacency matrix is a 2D array where each cell shows if an edge exists between two nodes.

Always initialize the matrix with zeros to avoid incorrect edge data.

Use matrix[i][j] = 1 to add an edge from node i to node j.

Be careful with indices to correctly represent edges in the graph.

Printing the matrix helps visualize the graph connections clearly.