It's key to understand that nobody really knows what goes into PageRank. Many believe that there are dozens if not hundreds of factors, but that the roots go back to the original concept of linking. It's not just volume of links either. Thousands of links by unauthoritative sites might be worth a handful of links from sites ranked as authoritative.
Do you regularly publish helpful, useful articles, videos or other types of media that are popular and well produced? Do you write for actual human beings rather than the search engine itself? Well, you should. Latest research from Searchmetrics on ranking factors indicates that Google is moving further towards longer-form content that understands a visitor’s intention as a whole, instead of using keywords based on popular search queries to create content.
A backlink is a reference comparable to a citation. The quantity, quality, and relevance of backlinks for a web page are among the factors that search engines like Google evaluate in order to estimate how important the page is. PageRank calculates the score for each web page based on how all the web pages are connected among themselves, and is one of the variables that Google Search uses to determine how high a web page should go in search results. This weighting of backlinks is analogous to citation analysis of books, scholarly papers, and academic journals. A Topical PageRank has been researched and implemented as well, which gives more weight to backlinks coming from the page of a same topic as a target page. 
It is interesting to read the article which however as others have commented leaves questions unanswered. The ideal internal page rank flow is clearly down the hierarchy and back up again evidently and no page to page links down the line. If this effect is big enough to have provoked an algorithm change then it must be substantial. Removing those related product links altogether would improve ranking and degrade the user experience of the site which surely is undesirable. I suspect the lesser of two evils was chosen.
Matt, my biggest complaint with Google and this “page Rank” nofollow nightmare is it seems we need to have a certain type of site to get ranked well or to make your crawler happy, you say you want a quality site, but what my users deem as quality (3000 links to the best academic information on the planet for business development) is actually looked at by Google as a bad thing and I do not get any rank because of it, makes it hard for my site to be found, and people that can really use the information can not find it when you yourself would look at the info and think it was fantastic to find it all in one place.
The total number of backlinks can often include many links from the same referring domain or multiple referring domains. It’s common for referring domains to link back to your content if it is relevant, authoritative or useful in some way to their own domain. In an ideal world, that’s how backlinks are accumulated; unique content that other websites want to be associated with.
Thanks for the post Chelsea! I think Google is starting to move further away from PageRank but I do agree that a higher amoount of links doesn’t necessarily mean a higher rank. I’ve seen many try to shortcut the system and end up spending weeks undoing these “shortcuts.” I wonder how much weight PageRank still holds today, considering the algorithms Google continues to put out there to provide more relevant search results.
Optimization techniques are highly tuned to the dominant search engines in the target market. The search engines' market shares vary from market to market, as does competition. In 2003, Danny Sullivan stated that Google represented about 75% of all searches. In markets outside the United States, Google's share is often larger, and Google remains the dominant search engine worldwide as of 2007. As of 2006, Google had an 85–90% market share in Germany. While there were hundreds of SEO firms in the US at that time, there were only about five in Germany. As of June 2008, the market share of Google in the UK was close to 90% according to Hitwise. That market share is achieved in a number of countries.
“So what happens when you have a page with “ten PageRank points” and ten outgoing links, and five of those links are nofollowed? Let’s leave aside the decay factor to focus on the core part of the question. Originally, the five links without nofollow would have flowed two points of PageRank each (in essence, the nofollowed links didn’t count toward the denominator when dividing PageRank by the outdegree of the page). More than a year ago, Google changed how the PageRank flows so that the five links without nofollow would flow one point of PageRank each.”
Provide full functionality on all devices. Mobile users expect the same functionality - such as commenting and check-out - and content on mobile as well as on all other devices that your website supports. In addition to textual content, make sure that all important images and videos are embedded and accessible on mobile devices. For search engines, provide all structured data and other metadata - such as titles, descriptions, link-elements, and other meta-tags - on all versions of the pages.
6. Measurement and analysis. You won’t get far in SEO unless you know how to measure your results, interpret those results, and use your analysis to make meaningful changes to your approach. The best tool for the job is still Google Analytics, especially if you’re new to the game. Spend some time experimenting with different metrics and reports, and read up on Analytics knowledge base articles. There’s a deep world to dive into.
SEO techniques can be classified into two broad categories: techniques that search engine companies recommend as part of good design ("white hat"), and those techniques of which search engines do not approve ("black hat"). The search engines attempt to minimize the effect of the latter, among them spamdexing. Industry commentators have classified these methods, and the practitioners who employ them, as either white hat SEO, or black hat SEO. White hats tend to produce results that last a long time, whereas black hats anticipate that their sites may eventually be banned either temporarily or permanently once the search engines discover what they are doing.
Most people who used the Google Toolbar probably never went through the effort of enabling the PageRank meter, which Google offered as an incentive to web surfers, a way for them to understand the quality of pages encountered when browsing (and a way for Google to understand what people were viewing beyond Google itself). But one group was very inclined to make the effort: SEOs.
youfoundjake, those would definitely be the high-order bits. The fact that no one noticed this change means (to me) even though it feels like a really big shift, in practice the impact of this change isn’t that huge. By the way, I have no idea why CFC flagged you, but I pulled your comment out of the Akismet bin. Maybe some weird interaction of cookies with WordPress caching? Sorry that happened.
PageRank is one of many, many factors used to produce search rankings. Highlighting PageRank in search results doesn’t help the searcher. That’s because Google uses another system to show the most important pages for a particular search you do. It lists them in order of importance for what you searched on. Adding PageRank scores to search results would just confuse people. They’d wonder why pages with lower scores were outranking higher scored pages.