How to find branch co-ordinates and branching angles of skeletonized image

Hello, I am dealing with images of vessel network.I have skeletonized the image and found branchpoints and endpoints using bwmorph. I now want to find co-ordinates of individual branches and their branching angles. I tried subtracting initial skeletonised image with just branchpoints to find edges. However, 4-connectivity breaks lots of relevant branches whereas 8-connectivity treats some multiple branches as one. I also tried to dilate the branchpoints and perform above to get proper edges. However, the above method is causing little trouble as I need to find which branchpoint or edgepoint is a vertex for each edge. Does anyone have an alternate solution to finding vertices of branches and their branching angles? Thanks in advance.

- Ruchit