Google's founders, in their original paper,[18] reported that the PageRank algorithm for a network consisting of 322 million links (in-edges and out-edges) converges to within a tolerable limit in 52 iterations. The convergence in a network of half the above size took approximately 45 iterations. Through this data, they concluded the algorithm can be scaled very well and that the scaling factor for extremely large networks would be roughly linear in {\displaystyle \log n} , where n is the size of the network.
Assume a small universe of four web pages: A, B, C and D. Links from a page to itself are ignored. Multiple outbound links from one page to another page are treated as a single link. PageRank is initialized to the same value for all pages. In the original form of PageRank, the sum of PageRank over all pages was the total number of pages on the web at that time, so each page in this example would have an initial value of 1. However, later versions of PageRank, and the remainder of this section, assume a probability distribution between 0 and 1. Hence the initial value for each page in this example is 0.25.
I’ve seen so many cases of webmasters nofollowing legitimate external links it is not funny. Any external link on their site is nofollowed, even when quoting text on the other site. IMO, the original purpose of nofollow has long been defeated in specific industries. As more webmasters continue doing everything they can to preserve their pagerank, the effectiveness of nofollow will continue to erode.
Here’s my take on the whole pagerank sculpting situation. As I understand it, the basic idea is that you can increase your rankings in Google by channeling the page rank of your pages to the pages you want ranked. This used be done with the use of the ‘no folow’ tag. That said, things have changed, and Google has come out and said that the way ‘no follow’ use to work has changed. In short, using ‘no follow’ to channel that page rank juice is no longer as effective as it once was.
In December 2009, Google announced it would be using the web search history of all its users in order to populate search results.[32] On June 8, 2010 a new web indexing system called Google Caffeine was announced. Designed to allow users to find news results, forum posts and other content much sooner after publishing than before, Google caffeine was a change to the way Google updated its index in order to make things show up quicker on Google than before. According to Carrie Grimes, the software engineer who announced Caffeine for Google, "Caffeine provides 50 percent fresher results for web searches than our last index..."[33] Google Instant, real-time-search, was introduced in late 2010 in an attempt to make search results more timely and relevant. Historically site administrators have spent months or even years optimizing a website to increase search rankings. With the growth in popularity of social media sites and blogs the leading engines made changes to their algorithms to allow fresh content to rank quickly within the search results.[34]
Finally, it’s critical you spend time and resources on your business’s website design. When these aforementioned customers find your website, they’ll likely feel deterred from trusting your brand and purchasing your product if they find your site confusing or unhelpful. For this reason, it’s important you take the time to create a user-friendly (and mobile-friendly) website.
Another tool to help you with your link building campaign is the Backlink Builder Tool. It is not enough just to have a large number of inbound links pointing to your site. Rather, you need to have a large number of QUALITY inbound links. This tool searches for websites that have a related theme to your website which are likely to add your link to their website. You specify a particular keyword or keyword phrase, and then the tool seeks out related sites for you. This helps to simplify your backlink building efforts by helping you create quality, relevant backlinks to your site, and making the job easier in the process.
If you’re just getting started with SEO, you’re likely to hear a lot about “backlinks,” “external and internal links,” or “link building.” After all, backlinks are an important SEO ranking factor for SEO success, but as a newbie, you may be wondering: what are backlinks? SEO changes all the time — do backlinks still matter? Well, wonder no more. Say hello to your definitive guide to backlinks and their significance in SEO.
While most of the links to your site will be added gradually, as people discover your content through search or other ways and link to it, Google understands that you'd like to let others know about the hard work you've put into your content. Effectively promoting your new content will lead to faster discovery by those who are interested in the same subject. As with most points covered in this document, taking these recommendations to an extreme could actually harm the reputation of your site.
What I like the most about Monitor Backlinks is that we can keep track of every single link, and that we can see the status of those links when they change or become obsolete. The details and the whole overview of Monitor Backlinks, is exactly what I need and no more, because there are a lot of SEO programmes on the market today, which promise to do what's necessary, but don't. Monitor Backlinks is exactly what I need for my SEO, and no more than that needed.

What is a useful place in search results? Ideally, you need to be in the top three search results returned. More than 70% of searches are resolved in these three results, while 90% are resolved on the first page of results. So, if you’re not in the top three, you’re going to find you’re missing out on the majority of potential business—and if you’re not on the first page, you’re going to miss out on nearly all potential business.
You may not want certain pages of your site crawled because they might not be useful to users if found in a search engine's search results. If you do want to prevent search engines from crawling your pages, Google Search Console has a friendly robots.txt generator to help you create this file. Note that if your site uses subdomains and you wish to have certain pages not crawled on a particular subdomain, you'll have to create a separate robots.txt file for that subdomain. For more information on robots.txt, we suggest this Webmaster Help Center guide on using robots.txt files13.

All in all, PageRank sculpting (or whatever we should call it) didn’t really rule my world. But, I did think that it was a totally legitimate method to use. Now that we know the ‘weight’ leaks, this will put a totally new (and more damaging) spin on things. Could we not have just left the ‘weight’ with the parent page? This is what I thought would happen most of the time anyway.

For most parts the sophistication in this system is simplified here. I still have trouble understanding the difference between letting link flow withing my pages without thinking about a loop. For example, page A, B and C link to each other from all angles therefore the link points should be shared. But in this loop formula, page B does not link to A. It just goes to C and loops. How does this affect navigation bars? As you know they are meant to link stay on top and link to all pages. I’m lost.
Matt, in almost every example you have given about “employing great content” to receive links naturally, you use blogs as an example. What about people that do not run blog sites (the vast majority of sites!), for example an E-Com site selling stationary? How would you employ “great content” on a site that essentially sells a boring product? Is it fair that companies that sell uninteresting products or services should be outranked by huge sites like Amazon that have millions to spend on marketing because they cant attract links naturally? 

Should have added in my previous comment that our site has been established since 2000 and all our links have always been followable – including comment links (but all are manually edited to weed out spambots). We have never artificially cultivated backlinks but I have noticed that longstanding backlinks from established sites like government and trade organisations are changing to ‘nofollow’ (and our homepage PR has declined from 7 to 4 over the past 5 years). If webmasters of the established sites are converting to systems which automatically change links to ‘nofollow’ then soon the only followable links will be those that are paid for – and the blackhats win again.
Ian Rogers first used the Internet in 1986 sending email on a University VAX machine! He first installed a webserver in 1990, taught himself HTML and perl CGI scripting. Since then he has been a Senior Research Fellow in User Interface Design and a consultant in Network Security and Database Backed Websites. He has had an informal interest in topology and the mathematics and behaviour of networks for years and has also been known to do a little Jive dancing.

This still encourages larger, more professionally run websites not to ‘share the wealth’ of PageRank to other sites. How is a small niche website ever going to get decent results in SERPS if when a bigger site does link to it, it nofollows the link? Not passing any PageRank benefit, or anchor text through the link does nothing to encourage smaller more specialised sites – it encourages the bigger, broader sites to hoard the goodness.
And my vital question about Amazon affiliate links. I think many people also wonder about it as well. I have several blogs where I solely write unique content reviews about several Amazon products, nothing more. As you know, all these links are full of tags, affiliate IDs whatsoever (bad in SEO terms). Should I nofollow them all or leave as they are?
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.
The world is mobile today. Most people are searching on Google using a mobile device. The desktop version of a site might be difficult to view and use on a mobile device. As a result, having a mobile ready site is critical to your online presence. In fact, starting in late 2016, Google has begun experiments to primarily use the mobile version of a site's content41 for ranking, parsing structured data, and generating snippets.
“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” – it doesn`t make much sense. If a page isn`t helpful and should not show up on search results, the best option is to meta-noindex the page and disallow it on robots.txt.
A great number of people who deal with SEO confuse backlink building and backlink earning. These notions are different. What is backlink building? It means to create conditions for SEO backlink referring to your site. To earn a backlink means to deserve it. Is that really possible? Yes! If you want your site to be worth earning backlinks, you must do everything possible and impossible to please your guests and users.

I have a question. My site is in download/free resources niche, and I’m having some troubles figuring out link building opportunities. Most of the webmasters from other websites in this niche don’t really actively respond to my email. I guess it’s because this is a niche that people often build a high traffic website and leave it there as a passive income. Do you have any suggestion?

So, as you build a link, ask yourself, "am I doing this for the sake of my customer or as a normal marketing function?" If not, and you're buying a link, spamming blog comments, posting low-quality articles and whatnot, you risk Google penalizing you for your behavior. This could be as subtle as a drop in search ranking, or as harsh as a manual action, getting you removed from the search results altogether!
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