There are many people working on various aspects of DNA graphs - for example, there's now the FASTG format, a replacement for the FASTA format which is essentially a graph in text form: http://fastg.sourceforge.net/

Some assemblers (SPAdes?) have started to support this format, but most downstream software only uses the FASTA format (the non-graph version from a single genome/representation).

Heng Li (somewhat now the godfather of bioinformatics) wrote a blog post about various implementations here: https://lh3.github.io/2014/07/25/on-the-graphical-representa...