Introduction to Graph Theory

1. Introduction to Graph Theory
With Real Life Example
Kazi Md. Sadiul
152-15-6254

2. Leonhard Euler
1707 - 1783
Father of graph theory

3. Overview
• What are graphs?
• Why study graph theory?
• Examples of graphs in the real world
• Different types of graphs
• Graphs programming tips

5. Node?
OR
Vertex ?

6. A

7. Edges

8. Edges
Unidirectional
Directional
Bidirectional

9. Directional VS Unidirectional

10. Weight OR Cast

11. Unidirectional Graph
A
B
C
D
E
F

12. Unidirectional Graph
Degree
Note That Unidirectional only Degree

13. Unidirectional Graph Degree(A)
deg(A) = {1}
C
A
B
D
E
F
C

14. Unidirectional Graph Degree(B)
deg(B) = {3}
C
A
B
D
E
F
C

15. Unidirectional Graph Degree(C)
deg(C) = {2}
C
A
B
D
E
F
C

16. Unidirectional Graph Degree(D)
deg(D) = {2}
C
A
B
D
E
F
C

17. Unidirectional Graph Degree(E)
deg(E) = {3}
C
A
B
D
E
F
C

18. Unidirectional Graph Degree(F)
deg(F) = {2}
C
A
B
D
E
F
C

19. Directional Graph

20. Directional Graph
A
B C
D
E
F

21. Directional Graph Degree
Note That Directional use inDegree and outDegree

22. In degree
In degree = 2
A
BC

23. Outer degree
Outer degree =3
A
B CE

24. Graph

25. Graph is high level data structure technic

26. A graph G consists of a set of vertices and a set of edges.
G = {V,E}
in this example,
V = {A,B,C,D,E,F},
Any graph can be drawn on paper in many ways – the important thing is
which vertices are connected (adjacent) to each other.
E = {AB, BC, BD, CD, DF, DE,EF}.

27. G = City
V = Note (Object)
In this example,
E = Edges(line)

29. Path

30. Path

31. Path
Cse 101
Cse 102 Cse 103
Cse 104 Cse 105 Cse 106 Cse 107
Book Set
C, c++

32. Path
C://
All
Program
Windows
Adobe Photos
hope
System32 Driver
Path C:Program FilesCommon Filesmicrosoft sharedMicrosoft Camera Codec Pack

33. Why study graph theory?
• Useful set of techniques for solving real-world problems –
particularly for different kinds of optimization.
• Graph theory is useful for analyzing “things that are
connected to other things”, which applies almost everywhere.
• Some difficult problems become easy when represented using
a graph.
• There are lots of unsolved questions in graph theory: solve
one and become rich and famous1

34. Why Study Graphs?
• Lots of problems formulated and solved in terms
of graphs
• – Shortest path problems
• – Network flow problems
• Matching problems
• Graph coloring problem
• Traveling Salesman Problem (TSP): still unsolved!
• and many more...

35. Examples of graphs in the real world

40. Structure of the internet

41. Maps

42. Programming exercises (Matplotlib)
• We’ll be using the Python language to work on applications
of
• graph theory.
• Windows installation files for Python and other required
libraries
• are on muele. Install Python, then the Network and
Matplotlib
• libraries.
• On Linux, installation is even easier as Python should
already
• be installed. To set up the extra libraries on Ubuntu:
• sudo apt-get install python-networkx python-matplotlib