Data are often represented as graphs. Many common tasks in data science are based
on distances between entities. While some data science methodologies natively take
graphs as their input, there are many more that take their input in vectorial form.
In this survey, we discuss the fundamental problem of mapping graphs to vectors, and
its relation with mathematical programming. We discuss applications, solution methods,
dimensional reduction techniques, and some of their limits. We then present an application
of some of these ideas to neural networks, showing that distance geometry techniques
can give competitive performance with respect to more traditional graph-to-vector