Meshes are, unlike nurbs, local controlled geometry. This means that density in one part of the mesh is not related to other parts. Because of this, meshes can represent much more complex shapes than nurbs surfaces (note that nurbs surfaces have limitions one will not find in polyBREP geometry which is based on nurbs surfaces). Meshes are a collection of faces (in the case of Rhino only 3- or 4-sided faces), where each face connects 3 or 4 vertices. In order to translate this into a network all we need to do is extract all the face edges (3 or 4 of them per face) and remove all the duplicate ones (bidirectional). In vbScript this is a rather expensive operation which is why the script caches the results in the mesh-object-data.
In the picture below consider the orange face. It connects the vertices 9, 11 and 44. The purple face to the right of the orange face connects vertices 11, 12 and 44 (presuming it's defined clockwise). These faces share the edge 11-44, eventhough they are in opposite directions.
Of course the above surface isn't a very interesting one and since meshes are capable of representing outrageous geometry, here a more thrilling example:
Prior to relaxation
.......
Relaxed state
For additional information.
