Section 8-6
Directed Graphs

Essential Question
• How do you use a picture, diagram, or
model to represent a real-world problem?
• Where you’ll see this:
• Sports, navigation, business

Directed Graph

Directed Graph
A geometrical representation of a map

Directed Graph
A geometrical representation of a map
A collection of points and arrows to show relationships

Example 1
In the diagram, A-G represent students, and the
arrows in the directed graph indicate that one
person knows the other person’s phone
number.
A
B C
D E F G

Example 1
How many phone numbers does B know?
A
B C
D E F G

Example 1
How many phone numbers does B know?
A
B C
D E F G

Example 1
How many phone numbers does B know?
A
B C
D E F G
B knows three numbers

Example 1
If E wanted to call G, how many calls would E
have to make to get G’s number?
A
B C
D E F G

Example 1
If E wanted to call G, how many calls would E
have to make to get G’s number?
A
B C
D E F G

Example 1
If E wanted to call G, how many calls would E
have to make to get G’s number?
A
B C
D E F G

Example 1
If E wanted to call G, how many calls would E
have to make to get G’s number?
A
B C
D E F G
E needs to make 2 calls to get G’s number

Example 1
What is the total number of direct calls that can be made
in this system?
A
B C
D E F G

Example 1
What is the total number of direct calls that can be made
in this system?
A
B C
D E F G
11 total direct calls can be made

Example 1
Create a matrix to describe this problem. Let 0 = the
cannot call that person and 1 = they can make that call.
A
B C
D E F G

Example 1
A
B C
D E F G

Example 1
A
B C
D E To F G
A B C D E F G
A 
 
B 
C 
From
 
D 
E 
 
F 
G




Example 1
A
B C
D E To F G
A B C D E F G
A 0 
 
B 0 
C 0 
From
 
D 0 
E 0 
 
F 0 
G 0


Example 1
A
B C
D E To F G
A B C D E F G
A 0 1 1 0 0 0 0
 
B 0 
C 0 
From
 
D 0 
E 0 
 
F 0 
G 0


Example 1
A
B C
D E To F G
A B C D E F G
A 0 1 1 0 0 0 0
 
B 0 0 1 1 1 0 0
C 0 
From
 
D 0 
E 0 
 
F 0 
G 0


Example 1
A
B C
D E To F G
A B C D E F G
A 0 1 1 0 0 0 0
 
B 0 0 1 1 1 0 0
C 0 0 0 0 0 1 1
From
 
D 0 1 0 0 1 0 0
E 0 1 0 1 0 0 0
 
F 0 0 0 0 0 0 0
G 0
 0 0 0 0 0 0


Problem Set

Problem Set
p. 359 #1-12
“Don’t worry about the world coming to an end today. It’s
already tomorrow in Australia.” - Charles M. Schulz