Data Structures and Algorithms
with Object-Oriented Design Patterns in Java 
One technique that is often used for a sparse graph, say 
,
uses 
linked lists--one for each vertex.
The linked list for vertex 
contains
the elements of 
,
the set of nodes adjacent to 
.
As a result, the lists are called
adjacency lists .
Figure 
shows the adjacency lists for the directed graph 
of Figure and the directed graph 
of Figure .
Notice that the total number of list elements used to represent
a directed graph is 
but the number of lists elements used to represent
an undirected graph is 
.
Therefore, the space required for the adjacency lists is 
.
By definition, a sparse graph has 
.
Hence the space required to represent a sparse graph
using adjacency lists is 
.
Clearly this is asymptotically better than using adjacency matrices
which require 
space.
Copyright © 1998 by Bruno R. Preiss, P.Eng. All rights reserved.
