6/15/2011
1
CS/ENGRD 2110
ObjectOriented Programming
and Data Structures
Spring 2011
Thorsten Joachims
Lecture 19:
Shortest Paths
Graph Definitions
•
A
directed graph
(or
digraph
) is a pair (V, E) where
–
V is a set
–
E is a set of ordered pairs (u,v) where u,v in V
•
Usually require u
≠
v (i.e., no selfloops)
•
An element of V is called a
vertex
(pl.
vertices
) or
node
•
An element of E is called an
edge
or
arc
•
V = size of V, often denoted
n
•
E = size of E, often denoted
m
2
b
a
c
d
e
f
Some Graph Terminology
•
Vertices u and v are called the
source
and
sink
of
the directed edge (u,v), respectively
•
Vertices u and v are called the
endpoints
of (u,v)
•
Two vertices are
adjacent
if they are connected by
an edge
•
The
outdegree
of a vertex u in a directed graph is
the number of edges for which u is the source
•
The
indegree
of a vertex v in a directed graph is the
number of edges for which v is the sink
•
The
degree
of a vertex u in an undirected graph is
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 ObjectOriented Programming, Graph Theory, Data Structures, shortest paths

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