Graphs

Vincent DUSAUTOIR | Antoine Foret

Summary

  • Graph THEORY

  • Different display

  • TYPES

  • ALGORITHMS

  • UTILITIES

GRAPH THEORY

STUDY GRAPH

A

B

C

D

X

NODE

LINK

DIFFERENT DISPLAY

A is LINKED with B

B IS LINKED WITH C

ADJacENCY MATRIX

A is LINKED with B

B IS LINKED WITH C

A B C

0 1 0

1 0 1

0 1 0

A

B

C

A B C

0 1 2

1 0 1

2 1 0

A

B

C

LABELED GRAPH

A is LINKED with B

B IS LINKED WITH C

A

B

C

TYPES

NULL

A

B

C

TRIVIAL

A

NON-DIRECTED

A

B

C

DIRECTED

A

B

C

CONNECTED

A

B

C

C

D

E

F

G

DISCONNECTED

A

B

C

C

D

E

F

G

COMPLETE

A

B

C

D

1

2

3

CYCLE

A

B

C

D

E

WHEEL

A

B

C

D

E

F

Cyclic

A

B

C

D

E

F

G

A-B-C-D-A

C-E-F-G-C

ACyclic

A

B

C

D

E

F

G

BIPARTITE

A

B

C

D

E

COMPLETE BIPARTITE

A

B

D

E

F

C

STAR GRAPH II

A

B

1

2

3

4

5

6

7

8

9

ALGORITHMS

DFS

Depth First Search

A

B

C

E

D

F

G

BFS

BREADTH FIRST SEARCH

A

B

C

E

D

F

G

DIJKSTRA

Edsger Wybe Dijkstra

A*

Peter E. Hart

Bertram Raphael

Nils J. Nilson

1968

1959

CONCRETE EXAMPLE

UTILITIES

MAPS

VIDEO GAMES

GENERATE TREE

+

*

3

8

3 * 8 + 12 / 3

/

12

3

24

4

28

OUR PROJECT

302 separation

A is friends with B

B is friends with C

C is friends with A

D is friends with A

A

B

C

D

ABCD

0111

1010

1100

1000

A

B

C

D

ABCD

0111

1012

1102

1220

A

B

C

D

Des questions ?

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