Is there an open source project that tries to replicate the Seven Bridges proprietary graphing technology? It seems like a logical next step.
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...
A novel data structure to store the whole graph: https://almob.biomedcentral.com/articles/10.1186/s13015-016-... Software is here: https://www.uni-ulm.de/in/theo/research/seqana.html
This one maps the whole DNA space using markers: http://www.nature.com/articles/ncomms7914
Here's a paper that looks at the total genetic space of several individuals, but with read mapping alone, no graphs: http://genomebiology.biomedcentral.com/articles/10.1186/s130...
Most of this is based on open source or openly available software. A big company that's closed source is NRGene from Israel, I've read good things about their DeNovoMAGIC/PanMAGIC but I'm unsure how that stuff works exactly (apart from massive short read coverage).
This is pretty close to my area...