If you are only thinking in terms of dimensions, then particles that are nano meters in size fall into the 'nano' category.
Most "regular" carbon has bonds that are random. In the case of graphite, bonds are primarily in one plane, and occasional bonds extending to planes above are below. These inter-plane are easily broken, providing a 'lubricating' effect. But all carbon has tremendous porosity or surface area, hence the ability to collect and filter.
If you are thinking in terms of the structural arrangement of nanotubes you are talking about something very different.
At a cost of $100 to $500 per Gram, it leads to a somewhat expensive filter.
Edit: Oops - I just found some 'short' nanotubes at $20/gram. So not so bad after all.