LGL used to work in such case for static visualizations - at least some years ago :)
http://lgl.sourceforge.net/
http://www.ncbi.nlm.nih.gov/pubmed/15184029?dopt=Abstract
I used it eg for a figure:
https://static-content.springer.com/image/art%3A10.1186%2F1471-2105-7-276/MediaObjects/12859_2006_Article_1015_Fig2_HTML.jpg
in the paper:
http://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-7-276
with data having a comparable number of nodes and edges.