Directed graphs

In a directed graph, the edges clearly show the direction from one vertex to another. An edge in a directed graph is usually represented as (v1, v2), which means that the edge is pointing from vertex v1 toward vertex v2. In other words, a (v1, v2) pair indicates that v1 is the starting vertex and v2 is the ending vertex. A directed graph is very useful in real-world applications and is used in the World Wide Web (WWW), Google's PageRank algorithm, and more. Consider the following directed graph:

Figure 10.1

Here, you can see an edge between vertices a and b. Because the edge is pointing from vertex a toward b, vertex a is considered to be the starting vertex and vertex b is considered the ending vertex. This edge can be represented as (a,b). Similarly, there is an edge from vertices a to c, which, in turn, can be represented as (a,c). Therefore, we can say that the preceding graph has the following set of vertices:

(V) - { a,b,c,d,e}

Additionally, the graph has the following set of edges:

(E) - {(a,b), (a,c), (c,d), (c,e), (d,b), (d,e), (e,a), (e,b)}