Directed Graph
🔹 What Is a Directed Graph?
A directed graph is made up of:
- Nodes (also called vertices) → These are like places, stations, or points.
- Directed edges (also called arcs) → These are like one-way roads connecting the places.
A directed edge has a start point and an end point.
So it tells you which direction you’re allowed to move.
🎯 Why Do We Need Direction?
Some relationships are not equal.
For example:
- You can follow someone on Instagram, but they may not follow you back.
- You can send a message to your teacher, but your teacher might not message you first.
- In a company, work flows from a manager → team leader → employee, not the other way around.
Whenever a relationship has a clear direction, a directed graph is a perfect way to model it.
📘 Simple Diagram of a Directed Graph
Here’s a small diagram you can easily visualize:
(A) ---> (B) ---> (C)
\ ^
\ |
-----> (D) ----What this diagram shows:
- There is a one-way connection from A to B.
- There is a one-way connection from B to C.
- A also connects to D.
- D connects back to C.
You can think of the arrows like traffic signs saying
“You can go this way but not the opposite way.”
🌱 Let’s Understand Through a Real-Life Example
📬 Email Flow
When you send an email:
- You → Your friend (one direction)
- Your friend may reply, but that is a separate direction.
So the email network forms directed edges from sender to receiver.
🎓 Classroom Example
Suppose you have a chain of command:
- Principal → Teacher → Class Monitor → Students
Again, each connection is one-way. That’s a directed graph.
🧠 Key Terms (Explained Simply)
1. Out-degree
How many arrows are leaving a node.
Example: If A has arrows going to B and D,
out-degree of A = 2.
2. In-degree
How many arrows are coming into a node.
Example: If C has arrows coming from B and D,
in-degree of C = 2.
3. Path (Directed Path)
A trail you follow by walking along the arrows.
Example: A → B → C is a directed path.
4. Cycle
A loop where you start at one node and come back to it by following directions.
Example: A → D → C → A forms a cycle if arrows allow it.
5. Directed Acyclic Graph (DAG)
A directed graph with no cycles.
Think of it like water flowing downhill — it never loops back.
🛠️ Where Are Directed Graphs Used?
You might be surprised — they’re everywhere!
- Google Maps (one-way streets)
- Social media following systems
- Course prerequisite chains
(You must complete Course A → before B) - Task scheduling
- Workflow diagrams
- Computer networks (data routing)
Whenever something moves from point A to point B with direction, a directed graph is quietly working behind the scenes.
About the Author
