Do links in hosted documents help with domain authority?
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When giving presentations in our industry, we often find that the PDF or PPT document is then hosted on the origination's domain for download by event attendees. If these files have links, do they count as inbound followed links?
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If these files have links, do they count as inbound followed links?
Yes, absolutely.
You can find links from .ppt .pdf .xls .doc and many other types of document files in your Google Webmaster tools account.
In addition, those documents accumulate PageRank and pass it. I have some PR6 .pdf documents. You can also optimize their document properties so that they will compete in the SERPs with a title tag of your choice.
If you publish these types of files, always put an attribution link to your website and don't hesitate to link to content on your website where it would be useful to readers.
If you are clever you can even place "Add to Cart" buttons in these documents.

I got into a Panda problem because I had a lot of duplicate content in .pdf documents - to control the scale and appearance of printed graphics. I was able to use .htaccess to apply rel=canonical to the .pdf documents and attribute them to specific html pages.
These documents can do just about anything that a webpage can do if you are clever.
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Great answer. I've seen some old PDFs on some .gov and .edu domains, but unfortunately, there were no URL links.