shortest paths through a point grid

Hello,
I have been trying to develop a definition that would find the shortest path through a disrupted point grid.
The purpose is to trace various urban flows (people, surface water, etc.).  This would seem to be the perfect project for Galapagos but so far the solution has remained out of reach. The attached file shows a point grid that has been randomly culled as a test case.  As a first step, I used the proximity component to determine the possible paths, setting this to only show orthogonal links. This, minor victory,however, was the extent of my success. I was hoping that someone might have some thoughts on this, and in so doing also offer more insight into the inscrutable operations of Galapagos.
Thanks for your consideration,
robin