This document discusses graphs as a non-linear, non-primitive, and dynamic data structure. It provides examples of graphs in maps, social networks, and operating systems. The document then covers graph types, representations using matrices and adjacency lists, traversal algorithms like breadth-first search and depth-first search, and comparing the two algorithms with examples.

1. Data Structure
GRAPH
1
5
Prepared by: Mir Omranudin Abhar
Email : MirOmran@Gamil.com
Spring , 2019

2. 2
Graph
• Non-Linear Data Structure
• Non- Primitive Data Structure
• Dynamic Data Structure

3. Google -Map
3

4. Facebook-Friends
4

5. Operating System
5

6. Graph
6

7. Graph-Type
7

8. Graph- Limitations
8

9. Graph- Complete Graph (Undirected )
9
𝑡𝑜𝑡𝑎𝑙 𝑒𝑑𝑔𝑒 =
𝑣(𝑣 − 1)
2

10. Graph- Complete Graph (Directed )
10
𝑡𝑜𝑡𝑎𝑙 𝑒𝑑𝑔𝑒 = 𝑣(𝑣 − 1)

11. Graph- Sub graph
11

12. Graph- Adjacent
12
𝐸𝑑𝑔𝑒 → 𝐵, 𝐷
𝑎𝑗𝑎𝑐𝑒𝑛𝑡 → (𝐵, 𝐷)

13. Graph- Simple ( Path )
13
Simple path: 𝑇ℎ𝑒 𝑃𝑎𝑡ℎ 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑟𝑒𝑝𝑒𝑎𝑡𝑟𝑒𝑑 𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠
𝑃𝑎𝑡ℎ → (𝐵, 𝐷, 𝐶, 𝐴)

14. Graph- Cycle ( Path )
14
Cycle:
𝑠𝑖𝑚𝑝𝑙𝑒 𝑝𝑎𝑡ℎ, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑣𝑒𝑟𝑡𝑒𝑥
𝑃𝑎𝑡ℎ → (𝐵, 𝐷, 𝐶, 𝐴, 𝐵)

15. Graph- (Connected & Non-Connected)
15
Non Connected Graph
Connected Graph
Strongly Connected

16. Graph- (Representation) - Matrix
16

17. Graph- (Representation) - Matrix
17

18. Graph- Adjacency Matrix Representation
of Graph
18

19. Graph- Adjacency List Representation of
Graph
19

20. Graph- Adjacency List Representation of
Graph
20

21. Graph- Adjacency List Representation of
Graph
21

22. Graph- Traversal Algorithm
22
• BFS (Breath First Search)
• DFS (Depth First Search)

23. Breadth first search (BFS)
23
Queue Data Structure : First in First Out

24. Breadth first search (BFS)
24
Time Complexity : O(bd)
Space Complexity : O(bd
)
b
:
‫اکثر‬ ‫حد‬
childe Node
‫که‬ ‫های‬
parent Node
‫داشته‬ ‫میتواند‬
‫باشد‬
.
d
:
‫کمترین‬ ‫تعداد‬
level
‫به‬ ‫رسیدن‬ ‫برای‬
node
‫یک‬ ‫در‬ ‫هدف‬
tree
.

25. Breadth first search (BFS) – Example[ 1 ]
25
Step: 1 BFS

26. Breadth first search (BFS) – Example[ 1 ]
26
Step: 2 BFS

27. Breadth first search (BFS) – Example[ 1 ]
27
Step: 3 BFS

28. Breadth first search (BFS) – Example[ 1 ]
28
Step: 4 BFS

29. Breadth first search (BFS) – Example[ 1 ]
29
Step: 5 BFS

30. Breadth first search (BFS) – Example[ 1 ]
30
Step: 6 BFS

31. Breadth first search (BFS) – Example[ 1 ]
31
Step: 7 BFS

32. Breadth first search (BFS) – Example[ 1 ]
32
Step: 8 BFS

33. Breadth first search (BFS) – Example[ 2 ]
33
BFS

34. Breadth first search (BFS) – Example[ 3 ]
34
BFS

35. Depth first search (DFS)
35
Stack Data Structure : Last in First Out

36. Depth first search (DFS)
36
Time Complexity : O(bm)
Space Complexity : O(b )
b
:
‫اکثر‬ ‫حد‬
childe Node
‫که‬ ‫های‬
parent Node
‫داشته‬ ‫میتواند‬
‫باشد‬
.
m
:
‫تمام‬ ‫مجموع‬
level
‫یک‬ ‫در‬ ‫ها‬
tree
.

37. Depth first search(DFS) – Example[ 1 ]
37
Step: 1 DFS

38. Depth first search(DFS) – Example[ 1 ]
38
Step: 2 DFS

39. Depth first search(DFS) – Example[ 1 ]
39
Step: 3 DFS

40. Depth first search(DFS) – Example[ 1 ]
40
Step: 4 DFS

41. Depth first search(DFS) – Example[ 1 ]
41
Step: 5 DFS

42. Depth first search(DFS) – Example[ 1 ]
42
Step: 6 DFS

43. Depth first search(DFS) – Example[ 1 ]
43
Step: 7 DFS

44. Depth first search(DFS) – Example[ 1 ]
44
Step: 8 DFS

45. Depth first search(DFS) – Example[ 1 ]
45
Step: 9 DFS

46. Depth first search(DFS) – Example[ 2 ]
46
DFS

47. Depth first search(DFS) – Example[ 3 ]
47
DFS

48. Compare (BFS & DFS) – example(1)
48

49. Compare (BFS & DFS) – example(2)
49

50. Question
.1
https://www.rollapp.com/
‫نماید‬ ‫تحقیق‬ ‫سایت‬ ‫این‬ ‫به‬ ‫ارتباط‬ ‫در‬
‫؟‬
.2
Big Data
‫چیست‬
,
‫نماید؟‬ ‫تحقیق‬
.3
‫اوردن‬ ‫بدست‬ ‫برای‬
value
‫ی‬ ‫ها‬
miss
‫در‬ ‫شده‬
database
‫ها‬ ‫الگوریتم‬ ‫کدام‬ ‫از‬
‫میشود‬ ‫استفاده‬
‫؟‬
50