Another fairly interesting application of graph theory in networking is with
bridges. When you have a collection of arbitrarily linked bridges, it is
really bad to have
loops.
That is why the
spanning tree algorithm is so important: it does the miracle of
pruning an arbitrary (possibly non-simple) connected graph into a
tree. And it can be
proven right !
Graph theory is also relevant to the study of queues, which are again very important in operating systems research.