People think about PageRank in lots of different ways. People have compared PageRank to a “random surfer” model in which PageRank is the probability that a random surfer clicking on links lands on a page. Other people think of the web as an link matrix in which the value at position (i,j) indicates the presence of links from page i to page j. In that case, PageRank corresponds to the principal eigenvector of that normalized link matrix.
Disclaimer: Even when I joined the company in 2000, Google was doing more sophisticated link computation than you would observe from the classic PageRank papers. If you believe that Google stopped innovating in link analysis, that’s a flawed assumption. Although we still refer to it as PageRank, Google’s ability to compute reputation based on links has advanced considerably over the years. I’ll do the rest of my blog post in the framework of “classic PageRank” but bear in mind that it’s not a perfect analogy.
Probably the most popular way to envision PageRank is as a flow that happens between documents across outlinks. In a recent talk at WordCamp I showed an image from one of the original PageRank papers:
In the image above, the lower-left document has “nine points of PageRank” and three outgoing links. The resulting PageRank flow along each outgoing link is consequently nine divided by three = three points of PageRank.
That simplistic model doesn’t work perfectly, however. Imagine if there were a loop:
No PageRank would ever escape from the loop, and as incoming PageRank continued to flow into the loop, eventually the PageRank in that loop would reach infinity. Infinite PageRank isn’t that helpful 
so Larry and Sergey introduced a decay factor--you could think of it as 10-15% of the PageRank on any given page disappearing before the PageRank flows along the outlinks. In the random surfer model, that decay factor is as if the random surfer got bored and decided to head for a completely different page. You can do some neat things with that reset vector, such as personalization, but that’s outside the scope of our discussion.
Now let’s talk about the rel=nofollow attribute. Nofollow is method (introduced in 2005 and supported by multiple search engines) to annotate a link to tell search engines “I can’t or don’t want to vouch for this link.” In Google, nofollow links don’t pass PageRank and don’t pass anchortext [*].
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.
Q: Why did Google change how it counts these links?
A: For one thing, some crawl/indexing/quality folks noticed some sites that attempted to change how PageRank flowed within their sites, but those sites ended up excluding sections of their site that had high-quality information (e.g. user forums).
Q: Does this mean “PageRank sculpting” (trying to change how PageRank flows within your site using e.g. nofollow) is a bad idea?
A: I wouldn’t recommend it, because it isn’t the most effective way to utilize your PageRank. In general, I would let PageRank flow freely within your site. The notion of “PageRank sculpting” has always been a second- or third-order recommendation for us. I would recommend the first-order things to pay attention to are 1) making great content that will attract links in the first place, and 2) choosing a site architecture that makes your site usable/crawlable for humans and search engines alike.
For example, it makes a much bigger difference to make sure that people (and bots) can reach the pages on your site by clicking links than it ever did to sculpt PageRank. If you run an e-commerce site, another example of good site architecture would be putting products front-and-center on your web site vs. burying them deep within your site so that visitors and search engines have to click on many links to get to your products.
There may be a miniscule number of pages (such as links to a shopping cart or to a login page) that I might add nofollow on, just because those pages are different for every user and they aren’t that helpful to show up in search engines. But in general, I wouldn’t recommend PageRank sculpting.
Q: Why tell us now?
A: For a couple reasons. At first, we figured that site owners or people running tests would notice, but they didn’t. In retrospect, we’ve changed other, larger aspects of how we look at links and people didn’t notice that either, so perhaps that shouldn’t have been such a surprise. So we started to provide other guidance that PageRank sculpting isn’t the best use of time. When we added a help page to our documentation about nofollow, we said “a solid information architecture — intuitive navigation, user- and search-engine-friendly URLs, and so on — is likely to be a far more productive use of resources than focusing on crawl prioritization via nofollowed links.” In a recent webmaster video, I said “a better, more effective form of PageRank sculpting is choosing (for example) which things to link to from your home page.” At Google I/O, during a site review session I said it even more explicitly: “My short answer is no. In general, whenever you’re linking around within your site: don’t use nofollow. Just go ahead and link to whatever stuff.” But at SMX Advanced 2009, someone asked the question directly and it seemed like a good opportunity to clarify this point. Again, it’s not something that most site owners need to know or worry about, but I wanted to let the power-SEOs know.
Q: If I run a blog and add the nofollow attribute to links left by my commenters, doesn’t that mean less PageRank flows within my site?
A: If you think about it, that’s the way that PageRank worked even before the nofollow attribute.
Q: Okay, but doesn’t this encourage me to link out less? Should I turn off comments on my blog?
A: I wouldn’t recommend closing comments in an attempt to “hoard” your PageRank. In the same way that Google trusts sites less when they link to spammy sites or bad neighborhoods, parts of our system encourage links to good sites.
Q: If Google changed its algorithms for counting outlinks from a page once, could it change again? I really like the idea of sculpting my internal PageRank.
A: While we can’t ever say that things will never change in our algorithms, we do not expect this to change again. If it does, I’ll try to let you know.
Q: How do you use nofollow on your own internal links on your personal website?
A: I pretty much let PageRank flow freely throughout my site, and I’d recommend that you do the same. I don’t add nofollow on my category or my archive pages. The only place I deliberately add a nofollow is on the link to my feed, because it’s not super-helpful to have RSS/Atom feeds in web search results. Even that’s not strictly necessary, because Google and other search engines do a good job of distinguishing feeds from regular web pages.
[*] Nofollow links definitely don’t pass PageRank. Over the years, I’ve seen a few corner cases where a nofollow link did pass anchortext, normally due to bugs in indexing that we then fixed. The essential thing you need to know is that nofollow links don’t help sites rank higher in Google’s search results.
