TITLE: Force-directed graph drawing in 1D?
QUESTION [6 upvotes]: I have a real-world graph that I wish to draw in one dimension.  Here's the graph:

I'd like to draw it using some kind of force-directed graph drawing method.  I'm supposing this is both possible and practical, but it may be that there's some obstacle I'm unaware of.  So, I'll begin with:

Question:  Is 1D force-directed graph drawing possible and practical?

And if so:

Question:  Does there exist software for force-directed graph drawing in 1D?

Gephi (among other packages) can provide a force-directed graph drawing in 2D, but I don't believe it can draw in 1D.
(Motivation: I'd like to see how similar the 1D force-directed drawing is to the drawing above, which places the vertices equispaced along the line, and in the order in which they are generated.)

REPLY [3 votes]: As an alternative to force-directed layout,
you might investigate the MinLA problem: the minimum linear arrangement problem for
nodes on a line. It plays a role in VLSI design. 
It is NP-hard but there are good approximation algorithms.
Here is one paper that will lead to many others:

Yehuda Koren and David Harel.
  "A Multi-Scale Algorithm for the Linear Arrangement Problem."
  Graph-Theoretic Concepts in Computer Science. Springer Berlin Heidelberg, 2002.
  (ACM link)

From its Introduction: