If you use Freebase search to get matches for any entity by name, you will get results sorted by relevance score. Try for example Taj Mahal.
I'm trying to get similar results using Freebase data dumps, so in my database 'Taj Mahal' related topics would be sorted by relevance, i.e. building comes first, musician comes next and so on.
Is there any suggestions how to achieve this without querying Freebase search API?
The wiki page on relevance score that you linked to says:
Freebase entities have an inherent relevance score (ranking) computed during indexing that is function of its inbound and outbound link counts in Freebase and Wikipedia. Some popular Freebase entities also have a popularity score computed by Google. By default, both scores are combined together during queries.
Which should give you a pretty good idea where to start. Freebase in-degree and out-degree can be computed directly from the dump, but Wikipedia in/out-degrees would require using the Wikipedia dump (or Freebase's WEX dump). The "popularity score computed by Google" piece is obviously something that you're not going to be able to replicate.
