Any web site that has many links incoming will have high page rank and pass more link juice. Educational institutions have an enormous amount of backlinks linking to them in a huge quantity and varieties.
Link juice is actually a calculation based among other things the incoming links to the domain. But edu sites allow very few outgoing links, so these links pass more link juice.
Anytime you build an .edu link behind a username and password it is probably not going to get indexed, and will do you no good.
Also it is not just a matter of PR, there can be two sites with the same PR and still one can have a huge amount more authority, making theory link more valuable. The Harvard law School has more authority than Houston community college. This means that a PR4 page on Harvard will pass more link juice than one from a PR 4 page in Houston CC, all other things equal.
Profile links, ,edu or not, are useless unless they are on a public page.