Adjacency Matrix Representation in DSA C# - Build from Scratch

Adjacency Matrix Representation

📖 Scenario: You are working on a simple social network app. Each person can be friends with others. You want to represent these friendships using a matrix where rows and columns represent people, and the value at each position shows if two people are friends.

🎯 Goal: Build an adjacency matrix to represent friendships between 4 people. Then, check if two specific people are friends.

📋 What You'll Learn

Create a 4x4 adjacency matrix with exact friendship connections

Add a variable to select two people to check friendship

Write logic to check if those two people are friends using the matrix

Print the friendship status clearly

💡 Why This Matters

🌍 Real World

Adjacency matrices are used in social networks, maps, and computer networks to represent connections between entities.

💼 Career

Understanding adjacency matrices helps in roles like software development, data analysis, and network engineering where graph data structures are common.

1

Create the adjacency matrix

Create a 2D integer array called adjacencyMatrix with 4 rows and 4 columns. Fill it exactly with these values:
0, 1, 0, 0
1, 0, 1, 1
0, 1, 0, 0
0, 1, 0, 0

DSA C#

// Your code here to create adjacencyMatrix

Hint

Use a 2D array with 4 rows and 4 columns. Each inner curly braces {} is a row.

2

Select two people to check friendship

Create two integer variables called personA and personB. Set personA to 0 and personB to 1 to represent the first and second person.

DSA C#

int[,] adjacencyMatrix = new int[4, 4]
{
    {0, 1, 0, 0},
    {1, 0, 1, 1},
    {0, 1, 0, 0},
    {0, 1, 0, 0}
};
// Your code here to create personA and personB

Hint

Use two integer variables to hold the indexes of the people you want to check.

3

Check if the two people are friends

Create a boolean variable called areFriends. Set it to true if adjacencyMatrix[personA, personB] equals 1, otherwise false.

DSA C#

int[,] adjacencyMatrix = new int[4, 4]
{
    {0, 1, 0, 0},
    {1, 0, 1, 1},
    {0, 1, 0, 0},
    {0, 1, 0, 0}
};

int personA = 0;
int personB = 1;
// Your code here to create areFriends

Hint

Use the matrix value at [personA, personB] to decide if they are friends.

4

Print the friendship status

Write a Console.WriteLine statement to print exactly: "Person 0 and Person 1 are friends: True" using the areFriends variable.

DSA C#

int[,] adjacencyMatrix = new int[4, 4]
{
    {0, 1, 0, 0},
    {1, 0, 1, 1},
    {0, 1, 0, 0},
    {0, 1, 0, 0}
};

int personA = 0;
int personB = 1;

bool areFriends = adjacencyMatrix[personA, personB] == 1;
// Your code here to print the friendship status

Hint

Use string interpolation with $"..." to include variables in the printed message.

Practice

1. What does an adjacency matrix represent in graph theory?

easy

A. A queue of nodes to visit

B. A list of nodes in the graph

C. A 2D array showing edges between nodes

D. A stack of visited nodes

Solution

1. Step 1: Understand adjacency matrix concept

   An adjacency matrix is a 2D array where rows and columns represent nodes.

2. Step 2: Identify what the matrix stores

   Each cell shows if an edge exists between two nodes (1 for edge, 0 for no edge).

3. Final Answer:

   A 2D array showing edges between nodes -> Option C

4. Quick Check:

   Adjacency matrix = 2D array of edges [OK]

Hint: Adjacency matrix is always a 2D array showing connections [OK]

Common Mistakes:

• Confusing adjacency matrix with adjacency list
• Thinking it stores node values instead of edges
• Mixing up matrix with traversal order

2. Which of the following is the correct way to declare an adjacency matrix for 4 nodes in C#?

easy

A. int[] matrix = new int[4];

B. int[,] matrix = new int[4,4];

C. int[][] matrix = new int[4];

D. int matrix = new int[4,4];

Solution

1. Step 1: Identify correct 2D array syntax in C#

   In C#, a 2D array is declared as int[,] with size [rows, columns].

2. Step 2: Check each option

   int[,] matrix = new int[4,4]; uses int[,] with size [4,4], correct for adjacency matrix of 4 nodes.

3. Final Answer:

   int[,] matrix = new int[4,4]; -> Option B

4. Quick Check:

   2D array syntax = int[,] [OK]

Hint: Use int[,] for 2D arrays in C# [OK]

Common Mistakes:

• Using jagged array syntax instead of 2D array
• Declaring 1D array for adjacency matrix
• Missing comma in array declaration

3. Given the following adjacency matrix for a graph with 3 nodes:

int[,] matrix = new int[,] {
  {0, 1, 0},
  {1, 0, 1},
  {0, 1, 0}
};

What is the output of Console.WriteLine(matrix[1,2]);?

medium

A. 1

B. 0

C. 2

D. Error

Solution

1. Step 1: Locate matrix element at row 1, column 2

   Matrix rows and columns start at 0, so matrix[1,2] is second row, third column.

2. Step 2: Check value at matrix[1,2]

   From the matrix, second row is {1, 0, 1}, third element is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   matrix[1,2] = 1 [OK]

Hint: Remember zero-based indexing for matrix rows and columns [OK]

Common Mistakes:

• Confusing row and column indices
• Assuming 1-based indexing
• Misreading matrix values

4. Identify the error in this C# code snippet for creating an adjacency matrix of 3 nodes:

int[] matrix = new int[3];
matrix[0,1] = 1;

medium

A. Incorrect array declaration syntax

B. No error, code is correct

C. Index out of range error

D. Cannot assign value to matrix[0,1]

Solution

1. Step 1: Analyze array declaration

   int[] matrix = new int[3]; declares a 1D array of 3 integers.

2. Step 2: Examine the assignment

   matrix[0,1] = 1; attempts to use 2D indexing on a 1D array, which is invalid in C#.

3. Final Answer:

   Cannot assign value to matrix[0,1] -> Option D

4. Quick Check:

   1D array indexing mismatch [OK]

Hint: 1D arrays cannot use [row,col] indexing [OK]

Common Mistakes:

• Using 2D indexing on 1D array
• Assuming jagged array syntax for 2D array
• Ignoring compiler error messages

5. You have a directed graph with 4 nodes. Which adjacency matrix correctly represents edges from node 0 to 1 and 2, and from node 3 to 0?

hard

A. int[,] matrix = new int[,] {
{0, 1, 1, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{1, 0, 0, 0}
};

B. int[,] matrix = new int[,] {
{0, 1, 0, 0},
{1, 0, 0, 0},
{1, 0, 0, 0},
{0, 0, 0, 1}
};

C. int[,] matrix = new int[,] {
{0, 0, 0, 1},
{1, 0, 0, 0},
{1, 0, 0, 0},
{0, 1, 1, 0}
};

D. int[,] matrix = new int[,] {
{0, 1, 1, 0},
{0, 0, 0, 1},
{0, 0, 0, 0},
{0, 0, 0, 0}
};

Solution

1. Step 1: Understand directed edges in adjacency matrix

   For directed graph, matrix[i,j] = 1 means edge from node i to node j.

2. Step 2: Check edges from node 0 to 1 and 2

   Row 0 should have 1s at columns 1 and 2.

3. Step 3: Check edge from node 3 to 0

   Row 3 should have 1 at column 0.

4. Step 4: Verify options

   int[,] matrix = new int[,] { {0, 1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0} }; matches all conditions exactly.

5. Final Answer:

   {{0, 1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}} -> Option A

6. Quick Check:

   Directed edges = matrix[i,j] = 1 [OK]

Hint: Row = from node, column = to node in adjacency matrix [OK]

Common Mistakes:

• Confusing rows and columns for direction
• Using symmetric matrix for directed graph
• Missing edges or adding extra edges