Adjacency Matrix Representation in DSA Javascript - Build from Scratch

Adjacency Matrix Representation

📖 Scenario: You are working on a simple social network app. You want to represent friendships between 4 friends using a matrix. Each friend is a node, and a friendship is a connection between nodes.

🎯 Goal: Create an adjacency matrix to show which friends are connected. Then, print the matrix to see the connections clearly.

📋 What You'll Learn

Create a 4x4 adjacency matrix named adjMatrix with exact values

Add a variable size to store the number of friends (4)

Use a nested for loop with variables i and j to print the matrix row by row

Print each row as a space-separated string of 0s and 1s

💡 Why This Matters

🌍 Real World

Adjacency matrices are used in social networks, maps, and computer networks to show connections between points.

💼 Career

Understanding adjacency matrices helps in roles like software development, data analysis, and network engineering where relationships between entities matter.

1

Create the adjacency matrix

Create a 4x4 adjacency matrix called adjMatrix with these exact rows:
[0, 1, 0, 1],
[1, 0, 1, 0],
[0, 1, 0, 1],
[1, 0, 1, 0]

DSA Javascript

// Your code here

Hint

Use a constant named adjMatrix and assign a 2D array with the exact rows shown.

2

Add the size variable

Create a constant called size and set it to 4 to represent the number of friends.

DSA Javascript

const adjMatrix = [
  [0, 1, 0, 1],
  [1, 0, 1, 0],
  [0, 1, 0, 1],
  [1, 0, 1, 0]
];
// Your code here

Hint

Use const size = 4; to store the number of friends.

3

Print the adjacency matrix

Use a nested for loop with variables i and j to iterate over adjMatrix and print each row as a space-separated string of 0s and 1s.

DSA Javascript

const adjMatrix = [
  [0, 1, 0, 1],
  [1, 0, 1, 0],
  [0, 1, 0, 1],
  [1, 0, 1, 0]
];
const size = 4;
// Your code here

Hint

Use two for loops: outer with i, inner with j. Build a string for each row and print it.

4

Print the final adjacency matrix output

Run the program to print the adjacency matrix rows exactly as space-separated 0s and 1s.

DSA Javascript

const adjMatrix = [
  [0, 1, 0, 1],
  [1, 0, 1, 0],
  [0, 1, 0, 1],
  [1, 0, 1, 0]
];
const size = 4;
for (let i = 0; i < size; i++) {
  let rowStr = '';
  for (let j = 0; j < size; j++) {
    rowStr += adjMatrix[i][j] + ' ';
  }
  console.log(rowStr.trim());
}
// Run the program to see the output

Hint

Check the console output matches the exact rows of the adjacency matrix.

Practice

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

easy

A. A 2D array showing connections between nodes

B. A list of nodes in the graph

C. A sequence of edges in order

D. A tree structure of nodes

Solution

1. Step 1: Understand adjacency matrix structure

   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 there is a connection (edge) between two nodes.

3. Final Answer:

   A 2D array showing connections between nodes -> Option A

4. Quick Check:

   Adjacency matrix = 2D array of connections [OK]

Hint: Adjacency matrix is always a 2D array of node links [OK]

Common Mistakes:

• Confusing adjacency matrix with adjacency list
• Thinking it stores node values instead of connections
• Assuming it is a sequence or tree

2. Which of the following is the correct way to declare a 3x3 adjacency matrix in JavaScript?

easy

A. const matrix = [0,0,0];

B. const matrix = [[0,0,0],[0,0,0],[0,0,0]];

C. const matrix = new Array(3);

D. const matrix = {0:0,1:0,2:0};

Solution

1. Step 1: Understand adjacency matrix as 2D array

   It must be an array of arrays, each inner array representing a row.

2. Step 2: Check each option's structure

   const matrix = [[0,0,0],[0,0,0],[0,0,0]]; is a 3x3 array filled with zeros, correct for adjacency matrix initialization.

3. Final Answer:

   const matrix = [[0,0,0],[0,0,0],[0,0,0]]; -> Option B

4. Quick Check:

   2D array syntax = const matrix = [[0,0,0],[0,0,0],[0,0,0]]; [OK]

Hint: Adjacency matrix needs nested arrays for rows and columns [OK]

Common Mistakes:

• Using a single array instead of 2D array
• Using object instead of array
• Creating array without inner arrays

3. What is the output of the following code?

const matrix = [
  [0, 1, 0],
  [1, 0, 1],
  [0, 1, 0]
];
console.log(matrix[1][2]);

medium

A. 1

B. 0

C. undefined

D. Error

Solution

1. Step 1: Identify indices in matrix

   matrix[1] is the second row: [1, 0, 1].

2. Step 2: Access element at column 2

   matrix[1][2] is the third element in second row, which is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   matrix[1][2] = 1 [OK]

Hint: Remember matrix[row][column] indexing starts at 0 [OK]

Common Mistakes:

• Confusing row and column indices
• Assuming 1-based indexing
• Expecting undefined for valid indices

4. Find the error in this adjacency matrix update code:

const matrix = [
  [0, 0],
  [0, 0]
];
matrix[0][1] = 1;
matrix[1][2] = 1;

medium

A. Matrix should be 1D array

B. Cannot assign value to matrix[0][1]

C. Index 2 is out of bounds for matrix[1]

D. No error, code is correct

Solution

1. Step 1: Check matrix dimensions

   Matrix has 2 rows and 2 columns (indices 0 and 1 only).

2. Step 2: Identify invalid index access

   matrix[1][2] tries to access third element in second row, which does not exist.

3. Final Answer:

   Index 2 is out of bounds for matrix[1] -> Option C

4. Quick Check:

   Accessing invalid column index = Error [OK]

Hint: Check array length before accessing indices [OK]

Common Mistakes:

• Ignoring array size limits
• Assuming dynamic resizing on assignment
• Confusing row and column indices

5. Given a graph with 4 nodes, how would you represent an undirected edge between node 1 and node 3 in an adjacency matrix?

hard

A. Set matrix[1][1] = 1 and matrix[3][3] = 1

B. Set matrix[1][3] = 1 only

C. Set matrix[3][1] = 1 only

D. Set matrix[1][3] = 1 and matrix[3][1] = 1

Solution

1. Step 1: Understand undirected edge representation

   Undirected edges are symmetric, so both directions must be marked.

2. Step 2: Mark both connections in matrix

   Set matrix[1][3] = 1 and matrix[3][1] = 1 to show connection both ways.

3. Final Answer:

   Set matrix[1][3] = 1 and matrix[3][1] = 1 -> Option D

4. Quick Check:

   Undirected edge = symmetric matrix entries [OK]

Hint: Undirected edges need two symmetric entries set [OK]

Common Mistakes:

• Setting only one direction for undirected edge
• Setting diagonal elements instead of edge
• Confusing node indices