It actually isn't all that difficult to prove. I have had several websites with hundreds of "un-themed" back links that were not spam but also not directly relevant. The site with those links hardly ever ranked well for primary keywords although they did rank fairly well for the themed keywords of the sites linking to them.
Conversely, I have had 2 "themed" back links to a website and have had that website rank for the primary terms within weeks regardless of how much PR the linking sites had.
It actually isn't all that difficult to prove. I have had several websites with hundreds of "un-themed" back links that were not spam but also not directly relevant. The site with those links hardly ever ranked well for primary keywords although they did rank fairly well for the themed keywords of the sites linking to them.
Conversely, I have had 2 "themed" back links to a website and have had that website rank for the primary terms within weeks regardless of how much PR the linking sites had.
Seems pretty cut and dry to me.
Note: This also seems to apply to internal links.
Seems to difficult to prove something like this. Surely it's just informed opinion and not evidence what people think?