When I look at https://en.wikipedia.org/w/api.php?action=query&prop=links&titles=Purdue%20University&pllimit=max I see a number of links to pages that do not appear on https://en.wikipedia.org/wiki/Purdue_University
The most obvious are a number of links to other Universities, such as the Columbia University and Colorado State University. Where are these coming from?
Links are defined as both direct links in the body of the article itself, as well as links found in templates that are embedded in the article. So, using the two you mentioned, both can be found linked at the very bottom of the article in the auto-hidden footer "Links to related articles", then either "Association of American Universities" or "Universities Research Association".