Is it possible to implement a Neural Network using a graph data structure? I'm trying to implement a feedforward neural network using a graph.
The thing is: I haven't found any example in which is used a graph data structure.
So far the examples I've found used arrays.

Can anyone please point me in the direction of some literature on the topic or some tutorial?
Many implementations you can find out in the web are done on matrices (MATLAB for instance) since it provides a compact notation. Haykin's textbook on neural networks takes this approach. Matrices also provide a simple translation to hardware design (FPGA, ASIC, etc.). They are also more often implemented on the FPU.

If you implement a neural network in an object oriented manner, you are effectively doing what your question asks: implementing a neural network on a graph. Your neurons are then objects that have relations with each others. There are a few books that take that approach. One I can think of is an undergrad level book by Renard called Réseaux de neurones (sorry, only in French).