5.4. Networks.   

If the number of vertices in a graph is V and the number of edges is E (0 <= E <= V(V-1)/2 , then graphs with all edges present are called complete. Graphs with relatively few edges are called sparse. Graphs with few missing edges are called dense or highly connected.

Sometimes it is useful to give each arc a value or weight: this may represent the cost of travelling on that route, the time taken, the distance, etc. A directed graph with weighted arcs is called a network.