1. Data Structures and Algorithms
Prof. Ajit A. Diwan
Prof. Ganesh Ramakrishnan
Prof. Deepak B. Phatak
Department of Computer Science and Engineering
IIT Bombay
Session: Graphs
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Graphs Useful to represent many real life situations
Family relationships
Road or rail network
Optimization problems
Minimize transportation costs and/or time
Shortest path problem
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Graphs A B E C D Vertex Each element / node in the graph
A, B, C, D, E are vertices of graph
Edge
Connection between two vertices
e.g. There is an edge between
A and B
A and C
B and D etc.
But, there is no edge for vertex E A B E C D E D G V
ERTEX V
ERTEX
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Undirected Graphs A B E C D Undirected Undirected edges
There is an edge from
A to B and B to A
A to C and C to A
B to D and D to B … A B E C D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Directed Graphs A B E C D Directed Directed edges
There is an edge from
A to B, but,
not from B to A
A to C and also from C to A
C to D, but
not from D to C A B E C D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Directed Graphs A B E C D Outgoing Edge
Directed edge from Source Vertex
A to C, C to D (but not from D to C)
Outgoing Degree
Number of edges from a Source Vertex
e.g.
A has 2 (B and C)
B has 0
C has 3 (A, B, and D) A B E C D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Directed Graphs A B E C D Incoming Edge
Directed edge to the Destination vertex
A to B, C to B, D to B
Indegree
Number of edges pointing to the Destination Vertex
e.g.
A has 1 (from C)
B has 3 (from A, C, and D) A B E C D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Thank you
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay