Practical applications of graphs usually require that they
be annotated with additional information.
Such information may be attached to the edges of the graph
and to the nodes of the graph.
A graph which has been annotated in some way is called a
*labeled graph* .
Figure shows two examples of this.

For example, we can use a directed graph with labeled vertices such as in Figure to represent a finite state machine. Each vertex corresponds to a state of the machine and each edge corresponds to an allowable state transition. In such a graph we can attach a label to each vertex that records some property of the corresponding state such as the latency time for that state.

We can use an undirected graph with labeled edges such as in Figure to represent geographic information. In such a graph, the vertices represent geographic locations and the edges represent possible routes between locations. In such a graph we might use a label on each edge to represent the distance between the end points.

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.