Adjacency List vs Matrix When to Choose Which in DSA Javascript - Build Both Approaches

Adjacency List vs Matrix: When to Choose Which

📖 Scenario: You are working on a simple social network app. You want to represent friendships between users. Some users have many friends, others have only a few. You want to learn how to store these friendships efficiently and understand when to use different methods.

🎯 Goal: Build two ways to represent friendships between 5 users: one using an adjacency list and one using an adjacency matrix. Then, decide which method is better for this social network.

📋 What You'll Learn

Create an adjacency list for 5 users with specific friendships

Create an adjacency matrix for the same 5 users with the same friendships

Add a variable to count total friendships

Write code to count friendships from the adjacency list

Print the adjacency list, adjacency matrix, and total friendships

💡 Why This Matters

🌍 Real World

Social networks, recommendation systems, and maps often use adjacency lists or matrices to represent connections between entities.

💼 Career

Understanding these structures helps in roles like software engineering, data science, and network analysis where graph data is common.

1

Create the adjacency list

Create a variable called adjList as an object representing friendships between 5 users (1 to 5). Use these exact friendships: 1 is friends with 2 and 3, 2 is friends with 1 and 4, 3 is friends with 1, 4 is friends with 2 and 5, 5 is friends with 4.

DSA Javascript

# Your code here

Hint

Use an object with keys 1 to 5. Each key has an array of friends.

2

Create the adjacency matrix

Create a variable called adjMatrix as a 2D array (array of arrays) representing the same friendships for users 1 to 5. Use 1 for friendship and 0 for no friendship. The rows and columns represent users 1 to 5 in order.

DSA Javascript

const adjList = {
  1: [2, 3],
  2: [1, 4],
  3: [1],
  4: [2, 5],
  5: [4]
};

# Your code here

Hint

Create a 5x5 array with 1s where users are friends and 0s elsewhere.

3

Count total friendships using adjacency list

Create a variable called totalFriendships and set it to 0. Then use a for loop with variables user and friends to iterate over Object.entries(adjList). Inside the loop, add the length of friends to totalFriendships.

DSA Javascript

const adjList = {
  1: [2, 3],
  2: [1, 4],
  3: [1],
  4: [2, 5],
  5: [4]
};

const adjMatrix = [
  [0, 1, 1, 0, 0],
  [1, 0, 0, 1, 0],
  [1, 0, 0, 0, 0],
  [0, 1, 0, 0, 1],
  [0, 0, 0, 1, 0]
];

# Your code here

Hint

Use Object.entries to get user and friends array, then add friends.length to totalFriendships.

4

Print the results

Write three console.log statements to print the adjList, adjMatrix, and totalFriendships variables in that order.

DSA Javascript

const adjList = {
  1: [2, 3],
  2: [1, 4],
  3: [1],
  4: [2, 5],
  5: [4]
};

const adjMatrix = [
  [0, 1, 1, 0, 0],
  [1, 0, 0, 1, 0],
  [1, 0, 0, 0, 0],
  [0, 1, 0, 0, 1],
  [0, 0, 0, 1, 0]
];

let totalFriendships = 0;
for (const [user, friends] of Object.entries(adjList)) {
  totalFriendships += friends.length;
}

# Your code here

Hint

Use console.log to print each variable on its own line.

Practice

1. Which data structure is generally better for representing a graph with many nodes but few edges?

easy

A. Adjacency Matrix

B. Adjacency List

C. Array

D. Stack

Solution

1. Step 1: Understand graph density

   A graph with many nodes but few edges is called a sparse graph.

2. Step 2: Choose efficient representation for sparse graphs

   Adjacency lists store only existing edges, saving space for sparse graphs.

3. Final Answer:

   Adjacency List -> Option B

4. Quick Check:

   Sparse graph = Adjacency List [OK]

Hint: Sparse graphs use adjacency lists for space efficiency [OK]

Common Mistakes:

• Choosing adjacency matrix for sparse graphs wastes space
• Confusing adjacency list with adjacency matrix
• Thinking arrays or stacks represent graphs directly

2. Which of the following is the correct syntax to initialize an empty adjacency list for a graph with 3 nodes in JavaScript?

easy

A. const graph = [[], [], []];

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

C. const graph = new Array(3).fill([]);

D. const graph = {};

Solution

1. Step 1: Understand adjacency list structure

   An adjacency list is an array where each element is an array of neighbors.

2. Step 2: Check each option

   const graph = [[], [], []]; creates separate empty arrays for each node. const graph = new Array(3).fill([]); fills with the same array reference, causing bugs.

3. Final Answer:

   const graph = [[], [], []]; -> Option A

4. Quick Check:

   Separate empty arrays = const graph = [[], [], []]; [OK]

Hint: Use separate empty arrays, not fill with one array [OK]

Common Mistakes:

• Using fill([]) which shares the same array reference
• Using adjacency matrix syntax for adjacency list
• Using an object instead of array for adjacency list

3. What will be the output of the following JavaScript code snippet?

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

medium

A. [0, 1, 2]

B. [0]

C. [1, 2]

D. undefined

Solution

1. Step 1: Understand the adjacency list structure

   graph[0] contains the neighbors of node 0, which are nodes 1 and 2.

2. Step 2: Check the console.log output

   Logging graph[0] prints the array [1, 2].

3. Final Answer:

   [1, 2] -> Option C

4. Quick Check:

   graph[0] = [1, 2] [OK]

Hint: Access adjacency list by index to get neighbors [OK]

Common Mistakes:

• Confusing adjacency list with adjacency matrix output
• Expecting all nodes instead of neighbors
• Mistaking graph[0] as undefined

4. Identify the error in this adjacency matrix initialization code for a graph with 3 nodes:

const graph = new Array(3).fill(new Array(3).fill(0));
graph[0][1] = 1;
console.log(graph);

medium

A. The inner arrays are shared references causing all rows to change

B. The graph array is not initialized with zeros

C. The syntax for new Array is incorrect

D. The assignment graph[0][1] = 1 is invalid

Solution

1. Step 1: Analyze array initialization

   Using fill with new Array(3).fill(0) creates one inner array shared by all rows.

2. Step 2: Effect of modifying graph[0][1]

   Changing graph[0][1] changes the same element in all rows because they reference the same array.

3. Final Answer:

   The inner arrays are shared references causing all rows to change -> Option A

4. Quick Check:

   Shared inner arrays cause unexpected changes [OK]

Hint: Use loop or map to create separate inner arrays [OK]

Common Mistakes:

• Assuming fill creates independent arrays
• Ignoring shared reference problem
• Thinking syntax is wrong instead of logic

5. You have a graph with 1000 nodes and about 10,000 edges. Which representation is more efficient in terms of memory and why? Choose the best option.

hard

A. Adjacency Matrix, because it allows O(1) edge checks

B. Adjacency List, because it stores all possible edges

C. Adjacency Matrix, because it is simpler to implement

D. Adjacency List, because it uses memory proportional to edges

Solution

1. Step 1: Calculate graph density

   Maximum edges for 1000 nodes is 1,000,000 (1000*1000). 10,000 edges is sparse.

2. Step 2: Compare memory usage

   Adjacency matrix uses memory for all possible edges (1,000,000). Adjacency list uses memory proportional to actual edges (10,000).

3. Step 3: Choose efficient representation

   Adjacency list is more memory efficient for sparse graphs.

4. Final Answer:

   Adjacency List, because it uses memory proportional to edges -> Option D

5. Quick Check:

   Sparse graph = Adjacency List memory efficient [OK]

Hint: Sparse large graph? Use adjacency list for memory [OK]

Common Mistakes:

• Choosing adjacency matrix for sparse graphs wastes memory
• Confusing simplicity with efficiency
• Thinking adjacency list stores all possible edges