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What do experts think?
take a page from category 1 and link from it to randomly selected pages from categories 2-6
I'm not sure I understand the random element to the linking - IMO you'd be better off linking pages in category 1 to other pages within category 1. The ideal would be to interlink content that was more closely related, or based on how important a particular content item is within your site.
If you link between related themes, then the things you discuss most often naturally acquire a greater volume of links, and this is as it should be. You risk losing any kind of genuine hierarchy if you randomly link between unrelated content.