regionprops() lists what it can measure in the "operations" list. It can measure things like area, perimeter, etc. You might also want to consider bwmorph() which can measure things like number of branchpoints or endpoints.
My File Exchange has an image segmentation tutorial that shows you how to use regionprops(). http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A31862