Graphs In Data Structure

Graphs - Introduction
Terminology
Graph ADT
Data Structures
Reading: 12.1-12.2
COSC 2011, Summer 2004

Definition
• A graph is a pair (V, E), where
– V is a set of nodes, called vertices
– E is a collection of pairs of vertices, called edges

• Both are objects (i.e. store data)
G

E

B

F
A
Vertex city computer web page airport C

D

COSC 2011, Summer 2004

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Edge
road cable hyperlink flight Example Applications
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•

•

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Electronic circuits
– Printed circuit board
– Integrated circuit
Transportation networks
– Highway network
– Flight network
Computer networks
– Local area network
– Internet
– Web
Databases
– Entity-relationship diagram
Questions
– Are two points connected?
– What is the shortest path between them? cslab1a

cslab1b math.brown.edu cs.brown.edu

brown.edu qwest.net att.net

cox.net
John
Paul

COSC 2011, Summer 2004

David

Types of edges
• Undirected edge {u,v}
– Does not indicate direction
– We can “travel” in either direction

A

B

• Directed edge (u,v)
– Has a direction
A
– We can only “travel” in one direction along the edge

B

• Self-loop
– Edge that originates and ends at the same vertex

• Parallel edges

A

– Two undirected edges with same end vertices
– Two directed edges with same origin and destination
COSC 2011, Summer 2004

A

B

Types of graphs
• Undirected graph
– All edges are undirected

• Directed graph
– All edges are directed

• Mixed graph
– Has both directed and undirected edges

• Simple graph
– No parallel edges and self-loops
COSC 2011, Summer 2004

Example find route from C to G
G

E

B

F
A

C

D

H
G

E

B

F
A

C

D
COSC 2011, Summer 2004

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Vertices and Edges
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•
•
•
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•

End vertices (or endpoints) of an edge
– U and V are the endpoints of a
Edges incident on a vertex - all edges that have the vertex as endpoint
– a, d, and b are incident on V
Adjacent vertices - endpoints of the same edge
– U and V are adjacent
Degree of a vertex - number of edges incident
V
h b a
– X has degree 5
Parallel edges
U
X