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Graph
A data structure
that consists of a set of
nodes and a set of edges
that relate the nodes to
each other
Vertex
A node in a
graph
Edge (Arc)
A pair of
vertices representing a
connection between two
nodes in a graph
Undirected graph
A
graph in which the
edges have no direction
Directed graph
(Digraph)
A graph in
which each edge is
directed from one vertex
to another (or the same)
vertex
310
Chapter 9
Abstract Data Types and Algorithms
Graphs
Trees are a useful way to represent relationships in which a hierarchy
exists. That is, a node is pointed to by at most one other node (its parent).
If we remove the restriction that each node may have only one parent
node, we have a data structure called a
graph
. A graph is made up of a set
of nodes called
vertices
and a set of lines called
edges
(or
arcs
) that
connect the nodes.
The vertices in the graph represent objects and the edges describe rela
tionships among the vertices. For instance, if the graph is representing a
map, the vertices might be the names of cities and the edges that link the
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 Fall '10
 MARIANAKANT

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