Graph Representation in C Using Adjacency Matrix

C Program to implement Graph Structure: Exercise-1 with Solution

Write a C program to represent a graph using an adjacency matrix.

From Wikipedia -

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.

The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information about the degree of each vertex.

Sample Solution:

C Code:

#include <stdio.h>

#define MAX_VERTICES 100

// Function to display the adjacency matrix
void displayGraph(int graph[MAX_VERTICES][MAX_VERTICES], int vertices) {
    printf("Adjacency Matrix:\n");
    for (int i = 0; i < vertices; i++) {
        for (int j = 0; j < vertices; j++) {
            printf("%d ", graph[i][j]);
        }
        printf("\n");
    }
}

// Function to add an edge to the graph
void addEdge(int graph[MAX_VERTICES][MAX_VERTICES], int start, int end) {
    graph[start][end] = 1;
    graph[end][start] = 1; // For undirected graph
}

int main() {
    int vertices, edges;

    // Input the number of vertices
    printf("Enter the number of vertices: ");
    scanf("%d", &vertices);

    if (vertices <= 0 || vertices > MAX_VERTICES) {
        printf("Invalid number of vertices. Exiting...\n");
        return 1;
    }

    int graph[MAX_VERTICES][MAX_VERTICES] = {0}; // Initialize the adjacency matrix with zeros

    // Input the number of edges
    printf("Enter the number of edges: ");
    scanf("%d", &edges);

    if (edges < 0 || edges > vertices * (vertices - 1) / 2) {
        printf("Invalid number of edges. Exiting...\n");
        return 1;
    }

    // Input edges and construct the adjacency matrix
    for (int i = 0; i < edges; i++) {
        int start, end;
        printf("Enter edge %d (start end): ", i + 1);
        scanf("%d %d", &start, &end);

        // Validate input vertices
        if (start < 0 || start >= vertices || end < 0 || end >= vertices) {
            printf("Invalid vertices. Try again.\n");
            i--;
            continue;
        }

        addEdge(graph, start, end);
    }

    // Display the adjacency matrix
    displayGraph(graph, vertices);

    return 0;
}

Output:

Enter the number of vertices: 5
Enter the number of edges: 7
Enter edge 1 (start end): 0 1
Enter edge 2 (start end): 0 2
Enter edge 3 (start end): 1 2
Enter edge 4 (start end): 1 3
Enter edge 5 (start end): 2 4
Enter edge 6 (start end): 3 4
Enter edge 7 (start end): 4 0
Adjacency Matrix:
0 1 1 0 1
1 0 1 1 0
1 1 0 0 1
0 1 0 0 1
1 0 1 1 0

Explanation:

In the exercise above,

• Header and Definitions:
• #include <stdio.h>: Includes the standard input-output library.
• #define MAX_VERTICES 100: Defines the maximum number of vertices in the graph.
• Function Declarations:
• displayGraph: Displays the adjacency matrix of the graph.
• addEdge: Adds an undirected edge between two vertices in the graph.
• Main Function (main):
• Declares variables 'vertices' and 'edges' to store the number of vertices and edges, respectively.
• Inputs the number of vertices from the user, checks for validity, and exits if invalid.
• Initializes a 2D array 'graph' (adjacency matrix) with zeros.
• Inputs the number of edges, checks for validity, and exits if invalid.
• Loops to input edges, validates vertices, and adds edges to the graph using "addEdge()" function.
• Displays the adjacency matrix using the "displayGraph()" function.
• Function Definitions (displayGraph and addEdge):
• displayGraph: Prints the adjacency matrix using nested loops.
• addEdge: Sets the corresponding matrix entries to 1 for an undirected edge.
• Input and Validation:
• Ensure that the user inputs are within valid ranges.
• Validates that edge vertices are within the range of vertices.
• Adjacency Matrix Initialization:
• Initializes the adjacency matrix with zeros.
• Graph Construction:
• Accepts edges from the user and adds them to the graph.
• Display:
• Prints the final adjacency matrix representing the graph.

Flowchart:

C Programming Code Editor:

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