Mobile Ad Hoc Networks

42  ◾  Mobile Ad Hoc Networks: Current Status and Future Trends

3.2.1.3 Undirected Graph

An undirected graph (UG) is described as G = (V, E), where V is the set of vertices or nodes

(V = {V

1

, V

2

, V

3

, …, V

N

}) and E is the set of edges between these vertices (E = {E

12

, E

21

, …}). E

xy

is an edge starting from vertex x and ending at vertex y. If there is a communication link between

V

1

and V

2

, then E є E

12

and E

21.

Since the graph is undirected, links are assumed to be starting

and ending on both sides. An example network with 10 nodes modeled with UG is depicted in

Figure 3.3. In this model, the set of vertices is V = {V

1

, V

2

, V

3

, …, V

10

} and the ...