It is well-known that the fundamental group of a finite, connected graph is a finitely generated free group, where one can take the chords of a spanning tree as a set of free generators. Diestel and Sprussel tried to give a similar combinatorial characterization of the end compactification of an infinite, locally finite, connected graph. They showed that the fundamental group embeds into a group of reduced words, where the words can have arbitrary countable order type and the notion of reduction is non-wellordered. Furthermore, they show that this group of reduced words embeds into an inverse limit of finitely generated free groups. In this talk, I will present a much simpler approach to this problem by showing how the fundamental group of the end compactification of a locally finite, connected graph embeds into the internal fundamental group of a hyperfinite (in the sense of nonstandard analysis) graph, which is then a hyperfinitely generated free group. I will discuss some applications of this result, including a simple proof that certain loops in the end compactification are non-nullhomologous. This is joint work with Alessandro Sisto.