Graphs consist of vertices connected by edges. Large graphs with billions of vertices are studied theoretically to understand their properties regardless of small changes in definition. There are different types of graphs including weighted, undirected, directed, connected, and complete graphs. Graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to search graphs, with DFS using a stack and BFS using a queue. Graph theory has applications in modeling networks, computer architectures, and optimization problems.

1. GRAPH

2. What is graph
Graphs consist of
 points called vertices
 lines called edges
1. Edges connect two vertices.
2. Edges only intersect at vertices.
3. Edges joining a vertex to itself are
called loops.

3. Example
FlexoFlexo BenderBender LeelaLeela
FryFry AmyAmy
This is also a graph. The vertices just happen to have
people’s names.
Such a graph could represent friendships (or any kind of
relationship).
FarnsworthFarnsworth
ZoidbergZoidberg

4. Theory of Large Graphs
Large graphs
 Billion vertices
 Exact edges present not critical
Theoretical basis for study of large graphs
 Maybe theory of graph generation
 Invariant to small changes in definition
 Must be able to prove basic theorems

5. Type of graph
Weighted Graph
Undirected Graph
Directed Graph
Connected Graphs
Complete Graphs

6. TRAVERSING A GRAPH
1.DFS:
DFS means death first search, we use
here STACK
2.BFS:
BFS means breath first search, we use
here QUEUE

7. DFS
Print :C STACK:E,F,D
Print:D STACK:E,F
Print:F STACK:E,I
Print:I STACK:E,H
Print:H STACK:E,G
Print:E STACK:B
Print:B STACK;
C,D,F,I,H,G,E
A
B C D
E
F G
I H

8. ADJACENCY LIST
A B,C,D H F,G
B C I H
C E,F,D
D F
E I,B
F I
G F,D
A
B C D
E
F G
I H

9. BFS

FRONT=1 QUEUE=A
REAR=1 ORIG= NULL
FRONT=2 QUEUE=A,B,C,D
REAR=4 ORIG=NULL, A,A,A
FRONT=3 QUEUE=A,B,C,D
REAR=4 ORIG=NULL,A,A,A,C
…………
FRONT=5 QUEUE=A,B,C,D,E,F,I
REAR=7 QUEUE=NULL,A,A,A,C,C,E
NOW USING BACK TRACK:
I –E –C-A
A
B C D
E
F G
I H

10. Some applications of Graph
Theory
 Models for communications and electrical
networks
 Models for computer architectures
 Network optimization models for
operations analysis, including scheduling
and job assignment
 Analysis of Finite State Machines
 Parsing and code optimization in
compilers

12. Adjacency list structure
coding

13. Any Question..??
THANK YOU