In my opinion, mapping can be very useful for Mathematics. Mapping is all about taking data and putting it in a form that is easier to view and understand. At the same time, Mathematics is all about finding data, and finding the connections and significance of that data. As usual, applied Mathematics might be greater benefited, in that the data relates to certain situations. Still, standard Mathematics is all about looking for relationships between equations. For example, when wanting to find and compare the derivative, or slope, of a function, f(x), at any given point of a curve, one could use mapping to compare all x- and y-values of the derivative. This could be used to find critical points, where the function is increasing and decreasing, etc.
From our use of the Gephi project in class, I find that such visualizations can be a link between many different fields, including but not limited to English, Mathematics, and Art. This combination allows people with different perceptions to look at the same image, and still comprehend it, rather than needing to put it in a different form. For example, one might have an image that depicts an analysis of a piece of literature. The English students can mouse over certain areas and look at the literary, historical, emotional, or other similarities between one piece and others. A mathematics student can consider the number of items that fall into any given category. A student of Art might look at the overall picture and, without regarding specific quantities or features, understand the general connections between any items depicted in the image.
I think that the use of mapping and social networking is a fun and sometimes-beneficial tool for expressing data. However, I do not think that it is always completely necessary. For example, a person wanting to compare connections between various airports in the United States (as we did in class) may see the mapping ability as very helpful in order to understand how one airport is connected to all others in a particular region. However, someone that wants to see information concerning a particular flight course may only want to see the stops from their departure to arrival, and not necessarily all the other cities that their departure airport goes to. Therefore, mapping may be more or less beneficial due to particular circumstances.