Extracting adjacency list from 2D and 3D skeleton images in python

Question

I have skeletonized 2D and 3D images as follows:

2D skeleton

3D skeleton

Now, I want to analyze the skeletons in python and obtain the following information:

1. The location of nodes.
2. The adjacency list.
3. The connectivity (the number of continuous skeletons in an image).

Is there any approach to do this in python?