Directed vs undirected graphs in Data Structures Theory - Quick Revision & Key Differences

Recall & Review

beginner

What is a directed graph?

A directed graph is a set of points called vertices connected by edges that have a direction. Each edge goes from one vertex to another specific vertex.

beginner

What is an undirected graph?

An undirected graph is a set of vertices connected by edges that do not have a direction. The connection between two vertices is mutual.

intermediate

How does edge direction affect graph traversal?

In directed graphs, you can only move along edges in their given direction. In undirected graphs, you can move freely between connected vertices both ways.

beginner

Give a real-life example of a directed graph.

A social media follower network is a directed graph because one person can follow another without the follow being mutual.

beginner

Give a real-life example of an undirected graph.

A friendship network is an undirected graph because friendship is usually mutual, so the connection goes both ways.

Which type of graph has edges with a specific direction?

A Both directed and undirected

B Undirected graph

C Directed graph

D Neither

Directed graphs have edges that point from one vertex to another, showing direction.

In an undirected graph, how do edges connect vertices?

A Edges have arrows showing direction

B Edges connect vertices mutually without direction

C Edges connect only one vertex

D Edges are not used

Undirected graph edges connect vertices in both directions equally.

Which graph type would best represent a one-way street map?

A Undirected graph

B Both

C Neither

D Directed graph

One-way streets have direction, so a directed graph models them well.

If you can travel back and forth freely between two points, the graph is likely:

A Undirected

B Weighted

C Directed

D Disconnected

Undirected graphs allow movement in both directions between connected vertices.

Which of these is NOT a property of directed graphs?

A Edges connect vertices mutually

B Edges can be one-way

C Edges have direction

D Edges go from one vertex to another

Directed graph edges do not necessarily connect vertices mutually; they have a specific direction.

Explain the main difference between directed and undirected graphs with examples.

Think about whether connections go one way or both ways.

Describe how edge direction affects movement in a graph.

Consider how you can travel between points.

Practice

1. Which of the following best describes a directed graph?

easy

A. Edges have a direction from one vertex to another

B. Edges connect vertices without any direction

C. Edges are weighted but have no direction

D. Edges connect only vertices of the same type

Solution

1. Step 1: Understand edge direction in graphs

   Directed graphs have edges that point from one vertex to another, showing direction.

2. Step 2: Compare with undirected graphs

   Undirected graphs have edges without direction, connecting vertices both ways equally.

3. Final Answer:

   Edges have a direction from one vertex to another -> Option A

4. Quick Check:

   Directed graph = edges with direction [OK]

Hint: Directed means edges point one way only [OK]

Common Mistakes:

• Confusing directed with weighted edges
• Thinking undirected edges have direction
• Assuming all graphs have directions

2. Which of the following is the correct way to represent an undirected edge between vertices A and B?

easy

A. (A → B) only

B. (A, B) only

C. (B, A) only

D. (A, B) and (B, A) both included

Solution

1. Step 1: Understand undirected edge representation

   Undirected edges connect two vertices both ways, so both (A, B) and (B, A) are included.

2. Step 2: Compare with directed edge representation

   Directed edges include only one direction, like (A → B), not both.

3. Final Answer:

   (A, B) and (B, A) both included -> Option D

4. Quick Check:

   Undirected edge = both directions stored [OK]

Hint: Undirected edges need both directions listed [OK]

Common Mistakes:

• Listing only one direction for undirected edges
• Confusing directed arrow notation with undirected
• Assuming undirected edges are stored once only

3. Given the directed graph edges: [(1, 2), (2, 3), (3, 1)], what is the result of checking if there is a path from vertex 3 to vertex 2?

medium

A. Only if the graph is undirected

B. Yes, there is a path

C. No, there is no path

D. Cannot determine without weights

Solution

1. Step 1: Analyze edges for path from 3 to 2

   Edges are (1 → 2), (2 → 3), (3 → 1). From 3, you can go to 1 only.

2. Step 2: Check if path leads to 2

   From 3 to 1, then from 1 to 2 is possible, so path exists: 3 → 1 → 2.

3. Final Answer:

   Yes, there is a path -> Option B

4. Quick Check:

   Path 3->1->2 exists [OK]

Hint: Follow edges direction step-by-step [OK]

Common Mistakes:

• Ignoring indirect paths
• Assuming no path if direct edge missing
• Confusing directed with undirected paths

4. Identify the error in this undirected graph edge list representation: edges = [(1, 2), (2, 3), (3, 1)] used as is for an undirected graph.

medium

A. Edges should be duplicated in reverse order

B. Edges must be tuples of length 3

C. Edges cannot connect vertex 3 to 1

D. No error, this is correct

Solution

1. Step 1: Understand undirected edge storage

   Undirected edges require both (u, v) and (v, u) to represent two-way connection.

2. Step 2: Check given edge list

   Edges are only listed one way, missing reverse edges like (2, 1), (3, 2), (1, 3).

3. Final Answer:

   Edges should be duplicated in reverse order -> Option A

4. Quick Check:

   Undirected edges need both directions [OK]

Hint: Undirected edges must appear both ways [OK]

Common Mistakes:

• Assuming one direction is enough
• Thinking tuples need 3 elements
• Believing given list is complete

5. You want to model a social network where friendships are mutual. Which graph type should you use and why?

hard

A. Directed graph, to track who follows whom

B. Directed graph, because friendships have direction

C. Undirected graph, because friendships go both ways

D. Weighted graph, to show friendship strength

Solution

1. Step 1: Understand the nature of friendships

   Mutual friendships mean if A is friend with B, then B is friend with A.

2. Step 2: Choose graph type matching mutual connections

   Undirected graphs represent mutual connections naturally, with edges having no direction.

3. Final Answer:

   Undirected graph, because friendships go both ways -> Option C

4. Quick Check:

   Mutual relations = undirected graph [OK]

Hint: Mutual means undirected edges [OK]

Common Mistakes:

• Choosing directed graph for mutual relations
• Confusing following with friendship
• Ignoring edge direction meaning