This document introduces graph theory and provides examples of graphs in the real world. It discusses how graphs are used to represent connections between objects and discusses some key graph concepts like nodes, edges, paths, and degrees. Real-world examples of graphs mentioned include social networks, maps, and the structure of the internet. The document also explains why graph theory is useful for modeling real-world networks and solving optimization problems.

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