Directed Graphs y = f(x) y (Digraphs) x Albert R Meyer March - - PowerPoint PPT Presentation

SLIDE 1

Mathematics for Computer Science

Normal Person’s Graph

MIT 6.042J/18.062J

y = f(x)

Directed Graphs

y

(Digraphs)

x

Albert R Meyer March 15, 2013

digraphs.1

Albert R Meyer March 15, 2013

digraphs.2

Computer Scientist’s Graph

Digraphs

a b

• a set, V, of vertices

c

• a set, E ⊆ V×V
• f directed edges

d f

(v,w) ∈ E notation: v→w

v w

e

Albert R Meyer March 15, 2013

digraphs.3

Albert R Meyer March 15, 2013

digraphs.4

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SLIDE 2

Relations and Graphs Digraphs

a b d c

V= {a,b,c,d} E = {(a,b), (a,c), (c,b)}

Albert R Meyer March 15, 2013

digraphs.5

Walks & Paths

Walk: follow successive edges length: 5 edges (not the 6 vertices)

Albert R Meyer March 15, 2013

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Formally, a digraph with vertices V is the same as a binary relation on V.

Albert R Meyer March 15, 2013

digraphs.6

Walks & Paths

Path: walk thru vertices

without repeat vertex

length: 4 edges

stuck!

Albert R Meyer March 15, 2013

digraphs.8

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SLIDE 3

• • • •
• •
• • • •
• •
• • • •
• •
• • • •
• •

Matrix representation Matrix representation

      1

• 
• 

         

• 
• 

    

• 
• 

     

• 
• 

              

• 
• 

     

• 

       

• 

                            

Albert R Meyer March 15, 2013

digraphs.9

Albert R Meyer March 15, 2013

digraphs.10

Matrix representation

Adjacency Matrix

 

 

• 

  1 1

• 

 1 1



• 



 

 

• 

1 1

• 

 

  



• 
• 

1









• 







• 



1

• 

                        



 



• 

 1  

• 

                          1 

Albert R Meyer March 15, 2013

digraphs.11

Albert R Meyer March 15, 2013

digraphs.12

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SLIDE 4

• • • •
• •

Adjacency Matrix

 

• 

 0 1 1  

•  0

1 1   

•  0

1   

•  0

1  

• 

 0 1  

• 

                          0 1 

Albert R Meyer March 15, 2013

digraphs.14

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SLIDE 5

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