A map of the Internet would be improbable with current technology. The Internet grows rapidly, and an accurate map of the Internet would have to grow with the same speed. This, combined with the possibility of private servers that cannot be accessed, makes a map of the Internet seem like the stuff of science fiction.
Despite this, several attempts to make a map of the Internet are in progress, and some even have experienced a degree of success. Any current attempt to create a map of the Internet, however, has only been able to show certain elements, such as the popularity of various Internet service providers (ISPs). None show every host and pathway through which data can travel.
A map of the Internet is also rather difficult to read, because it entails creating a two dimensional diagram of a two dimensional plane that overlaps a third dimensional plane. Therefore, some attempts to make a map of the Internet show a two-dimensional drawing, while others are pseudo-three-dimensional. This means that, even if a person cannot read one map of the Internet, he or she might be able to read another one.
Attempts to make a map of the Internet are also limited by computing power. In order to map out the pathways along which data can travel, one would need to trace every signal that goes into a server and then trace it to its source. This requires a lot of processing power, much more than the average desktop computer has. This is another reason why current technology limits the possibility of creating a map of the Internet. The only type of computer powerful enough to create a true map of the Internet would be a quantum computer, something that is mere theory in all but the most rudimentary applications.
In short, while a map of the Internet is theoretically possible, it cannot exist until computing advances beyond the relatively low-level plateau that it currently stands on.