Eberhard I von Thurgau - Zürichgau - Adalbert III Von Thurgau

The first clue that something is amiss is that the profile's name and display name don't match, Eberhard I vs. Eberhard II.

If you look at the About section we are blessed(?) that someone at some point has cut and paste the "source" they were using when building their tree. In it the father is shown as Adalhard not Adalbert.

The link to Medlands is a match for Adalbert but as you say their is no evidence of a son named Eberhard which corroborates the data in the About section.

What would really help would be to search Medlands for an Adalhard von Burc b: 0836 d: AFT 1 Jul 0874 with a son named Eberhard.

Here's a good place to start:

http://de.wikipedia.org/wiki/Adalhard_von_Burc

Swanaburc is a pretty unusual name so worth a search...

Which turns up Adelhard von Burc, abbé de Cysoing, not such a great help as they are floating loose :(

It's possible there is a link to this profile 50 or so years later
Hesso I, count in the Sülichgau

If you want to look further there maybe something here?

http://fmg.ac/Projects/MedLands/GERMAN%20NOBILITY.htm