Is there a matlab function to connect all the branches belonging to the same structure

I'm trying to classify artery and vein from retinal images using a semi-automatic method. I've already segmented the vessel, and next is to create a program that allows me to click on a vessel point and the entire vessel tree belonging this point are selected. like the image above. I feel like this is a simple task and can be achieved with a simple function but no idea where to start. Please help..

[Ashish Uthama]

What is the definition of a 'vessel tree'? Does the image on the left have two or three trees? Do you have any more information from the raw data or is your starting point just the binary mask (left image)? If it is, then I think this is not a simple task.