A network has N subscribers. Each subscriber is connected directly to all
other subscribers.
(a) What is the total number of lines L in the network?
(b) What is the value of L for N = 2, 10, 100, and 1,000?
(c) How many lines must be built to each subscriber?

Question

A network has N subscribers. Each subscriber is connected directly to all
other subscribers.
(a) What is the total number of lines L in the network?
(b) What is the value of L for N = 2, 10, 100, and 1,000?
(c) How many lines must be built to each subscriber?

mathmate · Answer

Since each subscriber is connected directly to all other subscribers, the network is a complete graph. Examples: |dw:1464491881364:dw| This is the same problem as a shake-hand problem in a party of N people. Every person must shake hands with N-1 people. But we're counting from both ends of the handshakes, so we have N(N-1)/2, dividing by two to adjust for it. Read about complete graphs in https://en.wikipedia.org/wiki/Complete_graph