The ShortestWalk add-on for Grasshopper exposes one component which, given a network of curves and a list of lines, calculates the shortest route from line start point to line end points in a network.
It is based on a topology calculator and the A* search algorithm.
- In Grasshopper, choose File > Special Folders > Components folder. Save the gha file there.
- Right-click the file > Properties > make sure there is no "blocked" text
- Restart Rhino and Grasshopper
Please let me know comments and ideas, and see also the Rhino ShortestWalk command. The source code for this command is published here.