I notice a lot of people have looked at this question but not answered - it may be confusion as to the reason for asking. I too am not sure why you need to know this as most of the Induction list vegetables have a lot of fiber. Where they sit on the Glycemic Index or Carb count is perhaps more important for LCers.

How about doing a net search on google.com and reporting back what you find?

I'd bet on celery - those strings must be completely fibre because they arent' digestible.

If you want ALL fibre, try Psyllium husk powder (available in capsules) from health food stores.