Graphs in social networks in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Graph Representation in Social Networks

In social networks, users and their connections can be represented as a graph. Which of the following best describes how a social network graph is typically represented?

A Nodes represent users and edges represent friendships or connections between users.

B Edges represent users and nodes represent the messages sent between them.

C Nodes represent messages and edges represent the time when messages were sent.

D Edges represent the number of posts a user has made, and nodes represent the user's profile.

💡 Hint

Think about what the main entities and their relationships are in a social network.

In social networks, each user is represented as a node (or vertex), and the connections or friendships between users are represented as edges (or links) connecting these nodes.

📋 Factual

intermediate

Types of Graphs in Social Networks

Which type of graph is most commonly used to represent mutual friendships in social networks?

A Tree graph where there is a single root user connected to all others.

B Directed graph where edges have a direction from one user to another.

C Weighted graph where edges represent the number of messages exchanged.

D Undirected graph where edges have no direction, representing mutual connections.

💡 Hint

Mutual friendships mean both users agree on the connection.

Mutual friendships are best represented by undirected graphs because the connection is two-way and does not have a direction.

🚀 Application

advanced

Analyzing Social Network Connectivity

Consider a social network graph where each node is a user and edges represent friendships. If a user has no edges connected to them, what does this imply about that user?

A The user has the most connections in the network.

B The user has no friends or connections in the network.

C The user is the central hub of the network.

D The user is connected to every other user in the network.

💡 Hint

Think about what it means to have zero edges connected to a node.

If a node has no edges, it means the user has no connections or friends in the social network graph.

🔍 Analysis

advanced

Impact of Removing a Node in a Social Network Graph

In a social network graph, what is the likely effect of removing a highly connected node (a user with many friends) on the overall network?

A The network becomes more connected because the node was blocking connections.

B There is no effect because nodes do not affect edges.

C The network may split into smaller disconnected groups or communities.

D The network automatically adds new edges to compensate.

💡 Hint

Consider what happens when a key user with many connections leaves the network.

Removing a highly connected node can break connections between groups, causing the network to split into smaller disconnected parts.

❓ Reasoning

expert

Determining the Shortest Path in a Social Network

In a social network graph, what does the shortest path between two users represent?

A The minimum number of connections needed to link the two users.

B The maximum number of friends one user has.

C The total number of users in the network.

D The number of messages exchanged between the two users.

💡 Hint

Think about how you might find the quickest way to reach a friend through mutual friends.

The shortest path is the smallest number of edges connecting two users, showing how closely they are linked through mutual friends.

Practice

1. In a social network graph, what do the nodes usually represent?

easy

A. Posts or comments

B. Users or people

C. Groups or communities

D. Messages sent

Solution

1. Step 1: Understand graph components in social networks

   Graphs use nodes to represent entities. In social networks, these entities are usually users or people.

2. Step 2: Identify what edges represent

   Edges represent connections like friendships, not the nodes themselves.

3. Final Answer:

   Users or people -> Option B

4. Quick Check:

   Nodes = Users [OK]

Hint: Nodes = users, edges = friendships [OK]

Common Mistakes:

• Confusing nodes with edges
• Thinking nodes represent messages
• Mixing up groups with nodes

2. Which of the following correctly describes an undirected edge in a social network graph?

easy

A. It shows a mutual friendship between two users

B. It represents a user posting a message

C. It shows a one-way friendship from one user to another

D. It indicates a user joining a group

Solution

1. Step 1: Define undirected edge meaning

   An undirected edge means the connection goes both ways, showing mutual relationship.

2. Step 2: Apply to social network context

   In social networks, mutual friendship means both users are connected equally, matching undirected edges.

3. Final Answer:

   It shows a mutual friendship between two users -> Option A

4. Quick Check:

   Undirected edge = mutual friendship [OK]

Hint: Undirected edges mean two-way connections [OK]

Common Mistakes:

• Thinking undirected edges are one-way
• Confusing edges with user actions
• Mixing edges with posts or groups

3. Consider this simple social network graph represented as adjacency list:
{'Alice': ['Bob', 'Carol'], 'Bob': ['Alice'], 'Carol': ['Alice']}
How many direct friends does Alice have?

medium

A. 2

B. 1

C. 3

D. 0

Solution

1. Step 1: Read Alice's adjacency list

   Alice's list shows ['Bob', 'Carol'], meaning Alice is directly connected to Bob and Carol.

2. Step 2: Count direct friends

   There are 2 names in the list, so Alice has 2 direct friends.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Length of Alice's list = 2 [OK]

Hint: Count names in adjacency list for direct friends [OK]

Common Mistakes:

• Counting indirect friends
• Confusing keys with values
• Ignoring list length

4. Given this adjacency list for a social network:
{'Dave': ['Eve'], 'Eve': ['Dave', 'Frank'], 'Frank': ['Eve']}
What is wrong if we add 'Frank' to Dave's list but forget to add 'Dave' to Frank's list?

medium

A. The graph will have a syntax error

B. The graph will show no connection between Dave and Frank

C. The graph becomes directed, showing one-way friendship

D. The graph will crash when accessed

Solution

1. Step 1: Understand undirected graph rules

   In undirected graphs, edges must be mutual. Adding Frank to Dave's list but not Dave to Frank's breaks this.

2. Step 2: Identify effect on graph type

   This creates a one-way connection, making the graph directed for that edge.

3. Final Answer:

   The graph becomes directed, showing one-way friendship -> Option C

4. Quick Check:

   Missing mutual edge = directed edge [OK]

Hint: Mutual edges needed for undirected graphs [OK]

Common Mistakes:

• Expecting syntax errors
• Assuming no connection exists
• Thinking graph will crash

5. A social network wants to suggest new friends by finding users who share at least two mutual friends but are not directly connected. Which graph concept helps solve this problem?

hard

A. Calculating node degrees

B. Finding shortest paths between nodes

C. Detecting cycles in the graph

D. Counting common neighbors between nodes

Solution

1. Step 1: Understand the friend suggestion criteria

   The network wants to find users not directly connected but sharing at least two mutual friends.

2. Step 2: Identify graph concept matching criteria

   Counting common neighbors (shared friends) between two nodes helps find such pairs.

3. Final Answer:

   Counting common neighbors between nodes -> Option D

4. Quick Check:

   Mutual friends = common neighbors [OK]

Hint: Mutual friends = common neighbors count [OK]

Common Mistakes:

• Using shortest paths incorrectly
• Confusing cycles with mutual friends
• Only checking node degrees