Network mapping or Internet Mapping is the study of the physical connectivity of the Internet. It is not to be confused with the remote discovery of which operating system a computer is running, an activity more akin to hacking.
Images of some of the first attempts at a large scale map of the internet were produced by the Internet Mapping Project and appeared in Wired magazine. The maps produced by this project were based on the layer 3 or IP level connectivity of the Internet (see OSI model), but there are different aspects of internet structure that have also been mapped.
More recent efforts to map the internet have been improved by more sophisticated methods, allowing them to make faster and more (comparatively)sensible maps. An example of such an effort is the OPTE project (see link below), which is attempting to develop a system capable of mapping the internet in a single day.
Graph theory can be used to better understand maps of the internet and to help choose between the many ways to visualize internet maps. Some projects have attempted to incorporate geographical data into their internet maps (for example, to draw locations of routers and nodes on a map of the world), but some projects are only concerned with representing the more abstract structures of the internet.