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Final Year Defense
1
Class presentation
Topics:
• Strongly connected graph
• Strongly Connected Components (SCC)
• Example.
• Breadth First Search (BFS)
Final Year Defense
2
Strongly connected graph
A directed graph is called strongly connected if for every
pair of vertices u and v there is a path from u to v and a path
from v to u.
Strongly Connected Components (SCC)
The strongly connected components (SCC) of a directed
graph are its maximal strongly connected subgraphs.
Class presentation
Final Year Defense
3
Example
Class presentation
Final Year Defense
4
Step 1 : (a) Discover time, (b) Finish Time.
Stack
1/14
2/13 7/12
9/10
8/11
3/6
4/5
A
B
F
G
H
D
C
Class presentation
Push
Final Year Defense
5
Step 2: Reverse the direction of a graph
A
B F
H
G
D
C
Class presentation
Final Year Defense
6
Step 3: Pop the vertex from stack and find visited element.
SCC components are………
1> {A-C-D-B} Visited vertex={A,C,D,B,F,G,H}
2> {F}
3> {G}
4> {H}
Number of SCC = 4
Class presentation
Stack
A
B
F
G
H
D
C
Pop
Final Year Defense
7
Breadth First Search
Step 1: S A C
Step 2: A C B
Step 3: C B D E
Step 4: B D E
Step 5:
Step 6:
D E F
E F V
Step 7: F V
Class presentation

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Algorithm, Basic topic of algorithm

  • 1. Final Year Defense 1 Class presentation Topics: • Strongly connected graph • Strongly Connected Components (SCC) • Example. • Breadth First Search (BFS)
  • 2. Final Year Defense 2 Strongly connected graph A directed graph is called strongly connected if for every pair of vertices u and v there is a path from u to v and a path from v to u. Strongly Connected Components (SCC) The strongly connected components (SCC) of a directed graph are its maximal strongly connected subgraphs. Class presentation
  • 4. Final Year Defense 4 Step 1 : (a) Discover time, (b) Finish Time. Stack 1/14 2/13 7/12 9/10 8/11 3/6 4/5 A B F G H D C Class presentation Push
  • 5. Final Year Defense 5 Step 2: Reverse the direction of a graph A B F H G D C Class presentation
  • 6. Final Year Defense 6 Step 3: Pop the vertex from stack and find visited element. SCC components are……… 1> {A-C-D-B} Visited vertex={A,C,D,B,F,G,H} 2> {F} 3> {G} 4> {H} Number of SCC = 4 Class presentation Stack A B F G H D C Pop
  • 7. Final Year Defense 7 Breadth First Search Step 1: S A C Step 2: A C B Step 3: C B D E Step 4: B D E Step 5: Step 6: D E F E F V Step 7: F V Class presentation