how do i create a network / graph from nodes and lines?

Hi,

I am trying to make a logistic simulator and want to create a node/line network from a travelmap. The image displays the routes on the map whichhave different gray scales for different travelling speeds.

I used the help from "image analyst" (tx!) do extract nodes and labelled paths:

1. extract skeleton from image, converted to 1/0 binary (Black/White) matrix
2. extract branchpoints
3. extract line segments using dilated branchpoints
4. label line segments

bwSkel = bwmorph(binaryImage, 'skel', inf);
bp = bwmorph(bwSkel, 'branchpoints');
bI = bwSkel  & ~bwmorph(bp,'dilate');
labeledImage = bwlabel(bI);

I got this:

How do I create a node-network/graph from the branchpoints and linesegments which will allow me to use algo's like travelling salesman problem?

I want the salesman to travel from A to B constrained so that he has to visit one of a selected set of nodes (hubs) before continuing his journey to the endpoint. He may have multiple endpoints which he has to visit.