Application of Graph Theory in Transportation Networks

When trying to estimate the maximum number of people who can fly from a city Ci to a city Cj through different routes and airports, one can use a networks N as a model. Let us assume the source s, as the origin Ci of the trip and the sink t, as the destination Cj , and the remaining internal nodes vi are the intermediate airports. An arc a = (vi , vj) of N represents a direct flight from the city vi to the city vj and c(a) denotes the maximum number of seats available on a direct flight from vi to vj .