You might want to look into the work of Valdis Krebs (http://www.orgnet.com/), a consultant who works on social networks and how to make them more efficient. He uses mapping to show connections and routes between people, teams or organizations.

Since part of the web is the direct expression of people (weblogs, academic papers, ...), what he does seems quite related to mapping the web. Valdis is not trying to make his maps "look geographic" though.

Similarly, Casey Marshall's weblog picture shows connections that a directory wouldn't reveal.
http://www.dcs.ed.ac.uk/cgi/csm/wlm

Hmm, can a map not look geographic?
http://www.dictionary.com/cgi-bin/dict.pl?term=map

Are these schemas too abstract to be called maps?
http://www.dictionary.com/cgi-bin/dict.pl?term=schema