Google has been internally using PageRank for a long time, so if I have two links in one paragraph, one is my an internal link to my website, and the second is an external link, does Google pass the same PageRank to both links?
Pagerank... is so the 90's. Google algorithm has come along way and pagerank no longer works the same as it once did. Its now one factor of over two hundred and is a minor factor, not a major factor like it used to be.
But to answer your question people have always believed that juice flows evenly and equally across internal and externally links on the page. Nofollow can be used on external links should you want to retain that juice. But I must express... PageRank is meaningless and you are best to focus your efforts on quality, diversity and relevance.
I recommend that you read some SEO guides written in the last couple of years, ideally the type of ones that do not even mention pagerank.
To support what Simon is saying, Google PageRank is not what you think it is nor is it as powerful as you think it is.
Links are important. High quality links are always gold. Make no mistake about that.
The PageRank calculation is now achieved using a proximity method that mirrors network trust models rather than being recursive. Essentially, the results are the same, however, if a new page appears, a PageRank for the page can be immediately applied instead of waiting. For the recursive calculation to work, all PageRank for all pages must be calculated over and over again (the recursive part) until the calculated difference is within a statistical range where the effect is essentially 0. This was run only quarterly originally, then less, and then adjusted to run more often. The recursive method ironically is fairly fast, but not efficient overall. Whereas the network trust proximity method is immediate and can be applied to just one page or as many as needed anytime.
PageRank is NOT what people think it is. A PR6 page with two links does not pass PR3 through each link. It is not that simple. Each site/page can have an authority cap applied. For example, PR6 is likely reduced when applying the PageRank calculations whereas PR1 will not be. As well, link quality is calculated based upon quite a few criteria and a value between 0 and .9 applied. So that PR6 with two links is passing much less than PR3 based upon the PR cap value and the link value which is less than 1. The reason for this is to apply a more natural curve to the PageRank calculation so that new pages can compete against super authorities. Otherwise, the PageRank algorithm can never work.
Lastly, consider that PageRank is not the sole pivotal metric. It never really was, however, with more metrics in play these days, it's importance has diminished quite a lot as it should. I want you to think in two parts. One is on the index side, and the other is on the query side. PageRank is applied to the index as many metrics are, however, many metrics are applied on the query side. For example, PageRank is calculated and applied within the index, and page relevance to the query is applied on the query side. Page relevance can easily override PageRank so that a page with a lower PR score can actually perform better for a particular query because it is more relevant.
Now to your question. Is the PR calculation applied to internal links different from all inbound and outbound links? (I cleaned it up a bit to make my point.) The answer is Yes. However, only in this regard. The PR model for all links in and out of a site starts with super authorities, those sites that rank extremely high such as Wikipedia, and is calculated from that starting point to include all links to and from any page as inbound and outbound links but not internal links. As for the PR calculation for internal links, they start at the home page and are limited to that site only not to include inbound or outbound links. Other than that, the PR caclutaions are the same. Clear? In otherwords, PR applied globally (across the whole web) is applied through a site whereas PR applied only to one site (internally) remains within the site.
No Google doesn't pass any page rank for both the links it completely depends on the DA of the website.
When you're giving internal link within your website...it has to be relevant and both the pages will perform well on Google. So, be careful when you're implementing internal & external links on the website.