How to get vertex position and connected vertices?

Have you looked into the Console output?
Using the factory settings, just paste the script into the text editor and run it.
It outputs the following:

No.; Name; Location x; Location y; Location z;
Object: Camera Type: CAMERA
Object: Cube Type: MESH
Processing mesh object: Cube
Mesh data: <bpy_struct, Mesh("Cube") at 0x000002AF47FCF208>
BMesh created
1; Cube; 1.00; 1.00; 1.00;
2; Cube; 1.00; 1.00; -1.00;
3; Cube; 1.00; -1.00; 1.00;
4; Cube; 1.00; -1.00; -1.00;
5; Cube; -1.00; 1.00; 1.00;
6; Cube; -1.00; 1.00; -1.00;
7; Cube; -1.00; -1.00; 1.00;
8; Cube; -1.00; -1.00; -1.00;
Object: Light Type: LIGHT