Directed Graph

Definition

A directed graph is a graph where edges have direction.

Example:

A -> B

This means the connection goes from A to B.

It does not automatically mean the connection goes from B to A.

Directed graph = graph with one-way edges.

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Direction Matters

In a directed graph:

A -> B

is different from:

B -> A

If both directions exist, both edges must be present:

A -> B
B -> A

Direction makes connection asymmetric unless the reverse edge is also defined.

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Directed Edges As Ordered Pairs

A directed edge can be represented as an ordered pair.

Example:

(A, B)

means:

A -> B

The first element is the starting node.

The second element is the ending node.

Directed edges use order to encode direction.

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Simple Examples

Directed graphs can represent relationships where direction matters.

Examples:

• web page links
• task dependencies
• one-way roads
• state transitions
• input-output flow

Example:

Task A -> Task B

can mean:

Task B depends on Task A

Directed graphs model structured movement or dependency.

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Incoming And Outgoing Edges

For:

A -> B

the edge is outgoing from A.

The edge is incoming to B.

This distinction matters when tracking flow through a graph.

Direction lets us ask where a connection comes from and where it goes.

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Final Summary

• A directed graph has edges with direction.
• A -> B is different from B -> A.
• Directed edges can be represented as ordered pairs.
• Directed graphs are useful for dependencies, links, transitions, and flow.
• Direction creates incoming and outgoing edges.