1. ICOM 4035 – Data Structures Lecture 15 – Graph ADT
Manuel Rodriguez Martinez
Electrical and Computer Engineering
University of Puerto Rico, Mayagüez
©Manuel Rodriguez – All rights reserved

2. Lecture Organization Part I – Introduction to the Graph ADT
Part II – Implementation of the Graph ADT using an adjacency lists
M. Rodriguez-Martinez
ICOM 4035

3. Objectives Introduce the concept of a graph
Collection of nodes interconnected by edges
Discuss design and implementation of graph adt
Provide motivating examples
M. Rodriguez-Martinez
ICOM 4035

4. Companion videos Lecture15 videos
Contains the coding process associated with this lecture
Shows how to build the interfaces, concrete classes, and factory classes mentioned here
M. Rodriguez-Martinez
ICOM 4035

5. Part I
Introduction to the Graph ADT
M. Rodriguez-Martinez
ICOM 4035

6. Uses of graphs Graphs Graphs are used to represent:
Collection of nodes connected by edges
G = (V,E)
V = collection of nodes
E = collection of edges
Graphs are used to represent:
Roads/airline routes between cities
Relationships between persons
Facebook friendship
Connections between computers on a network
Job scheduling
An many more …
M. Rodriguez-Martinez
ICOM 4035

7. Introduction to Graphs
San Juan
Bob
Hatillo
Fajardo
Apu
Ned
Aguadilla
Ponce
Money debtor
Mayaguez
Roads between cities
Collection of nodes interconnected by edges
M. Rodriguez-Martinez
ICOM 4035

8. Introduction to Graphs (2)
UPRRP
UPRM
UPR RCM
UPRA
UPR AC
Classic use for graphs: network modeling
M. Rodriguez-Martinez
ICOM 4035

9. Directed Graph Directed Graph
A Graph G=(V,E) is directed graph whenever the edges have an associated direction
i.e., edge (a,b) is different from (b,a) or (b,a) might not be present
Bob
Directed Graph
Apu
Ned
Money debtor
M. Rodriguez-Martinez
ICOM 4035

10. Undirected Graph Undirected Graph
San Juan
A Graph G=(V,E) is undirected graph whenever the edges have no associated direction
i.e., edge (a,b) is the same as (b,a)
Hatillo
Fajardo
Aguadilla
Ponce
Mayaguez
Roads between cities
Undirected Graph
M. Rodriguez-Martinez
ICOM 4035

11. Graph vs Tree A Tree is a special case of a undirected graph
In general, graphs:
Have no notion of root node
Have no notion of leaf nodes
Can have cycles
Can be disconnected
M. Rodriguez-Martinez
ICOM 4035

12. Disconnected Graph Notice that Aguadilla and Mayaguez are disconnected
San Juan
Hatillo
Fajardo
Notice that Aguadilla and Mayaguez are disconnected
Aguadilla
Ponce
Mayaguez
Roads between cities
M. Rodriguez-Martinez
ICOM 4035

13. Path in Graph
Path: Given a graph G = (V, E), a path P in G is a collection of edges P = {e1, e2, …, ek} such that e1 = (n1, n2), e2 (n2, n3), …, ek = (ni-1, ni).
A path is made by connecting consecutive edges
Alternative notation: P = {n1, n2, n3, ...,ni-1, ni}
Left to right order is important.
Leftmost starts the path
Paths can have cycles
One or more nodes repeat
M. Rodriguez-Martinez
ICOM 4035

14. Paths in a graph Example Paths:
San Juan
Example Paths:
P1 = {San Juan, Ponce, Mayaguez, Aguadilla, Hatillo, San Juan, Fajardo}
P2 = {Ponce, San Juan, Fajardo}
Hatillo
Fajardo
Aguadilla
Ponce
Mayaguez
Roads between cities
M. Rodriguez-Martinez
ICOM 4035

15. Part II Implementation of the Graph ADT using an adjacency lists
M. Rodriguez-Martinez
ICOM 4035

16. Representation of Graphs
There two main methods to implement Graphs
Adjacency Matrix
Adjacency List
M. Rodriguez-Martinez
ICOM 4035

17. Adjacency Matrix Bob Ned Apu 1 Bob Apu Ned You use a boolean matrix1
Bob
Apu
Ned
You use a boolean matrix
0 means there is no edge between nodes a,b
1 means there is an edge between nodes a,b
Wastes too much space if matrix is sparse
M. Rodriguez-Martinez
ICOM 4035

18. Adjacency Lists Bob Apu Ned You use an array of linked lists
Each node has a list with the nodes that
are adjacent to it.
Saves space, and is easier to implement.
M. Rodriguez-Martinez
ICOM 4035

19. Summary Introduced the concept a Graph Discussed application of Graphs
Unbalanced ordered tree
Discussed application of Graphs
Illustrated implementation of directed Graphs using adjacency lists
M. Rodriguez-Martinez
ICOM 4035

20. Questions? Email: manuel.rodriguez7@upr.edu M. Rodriguez-Martinez
ICOM 4035