7.1. Paths and Reachability
Definition 7.7 (Path)

Let G = (V, E, f) be a simple digraph.
A sequence of edges is called a path of G, if and only if
the terminal node of each edge in the path is the initial
node of the next edge, if any, in the path.
An example of such a path:

Definition 7.8 (Length of a Path)

The number of edges appearing in the sequence of a path is
called the length of a path.
Definition 7.9 (Cycle)

A path that originates and ends in the same node is called
a cycle.
A cycle is called simple if no edge in the cycle appears
more than once in the path.
A cycle is called elementary if it does not traverse
through any node more than once.
Definition 7.10 (Acyclic)

A simple digraph that does not have any cycles is called
acyclic.
Definition 7.11 (Path Relation)

Let G = (V, E) be a simple digraph.
The path relation P
of G is defined as
P = { (u,v)  there exists a path from node u to node v }
The path length from the node u to the node v
is called the distance and is denoted by d(u, v).
Created by unroff & hptools.
© by HansPeter Bischof. All Rights Reserved (1998).
Last modified: 27/July/98 (12:14)