TITLE: Etymology of "topological sorting"
QUESTION [20 upvotes]: This may be a dumb question, but what's "topological" about topological sorting in graph theory? 
I thought topology was related to geometry and deformations.

REPLY [5 votes]: The use of "topological" in "topological sorting" and "topological order" appears to stem from the use of the word "topology" to describe the structure of networks in computer science literature. Indeed, if you look at the early papers on topological sorting (Lassser, CACM, 1961; Kahn, CACM, 1962) you will see they are motivated by topological sorting of PERT charts (project management). A quick google books search shows even earlier analogous uses of "topology" in computer science, e.g. to describe the structure of electrical circuit networks.
Most likely the terminology became widely known after it was employed in Knuth's influential book The art of Computer Programming, vol. 1, 1967. Of course the phrase "network topology" is still in wide use today. 
More general mathematical results go back to at least to 1930, see the Szpilrajn extension theorem.