A very important networking algorithm (the spanning tree protocol) can very well be considered graph theory.

In the original work (Radia Perlman, An algorithm for distributed computation of a spanningtree in an extended LAN, SIGCOMM '85 Proceedings of the ninth symposium on Data communications) the algorithm is summarized as follows:

**Algorhyme**

I think that I shall never seea graph more lovely than a tree.
A tree whose crucial propertyis loop-free connectivity.
A tree that must be sure to spanso packets can reach every LAN.
First, the root must be selected.
By ID, it is elected.
Least-cost paths from root are traced.
In the tree, these paths are placed.
A mesh is made by folks like me,
then bridges find a spanning tree. 

A very important networking algorithm (the spanning tree protocol) can very well be considered graph theory.

In the original work (Radia Perlman, An algorithm for distributed computation of a spanningtree in an extended LAN, SIGCOMM '85 Proceedings of the ninth symposium on Data communications) the algorithm is summarized as follows:

**Algorhyme**

I think that I shall never see
  a graph more lovely than a tree.
A tree whose crucial property
  is loop-free connectivity.
A tree that must be sure to span
  so packets can reach every LAN.
First, the root must be selected.
  By ID, it is elected.
Least-cost paths from root are traced.
  In the tree, these paths are placed.
A mesh is made by folks like me,
  then bridges find a spanning tree.