Python zipfile whole path is in file

Question

I'm using the code from here to make a zip file from a directory. I give the function an absolute path to a folder from a GUI. Currently, say the path is c:\users......, the zip folder structure is users...... .

How can I remove the absolute path bits and just have the end folder of the path being used for the zip file? I understand that the result is right, because what I'm describing is the result from os.walk but I want to strip out the absolute path.

def zipdir(path, zip):
    for root, dirs, files in os.walk(path):
        for file in files:
            zip.write(os.path.join(root, file))