Page rank is an assessment of the authority and value of a website in Google’s algorithm. You can find plug-in tools for your browser or online tools (see the references section for links to some of these) to check the page rank of any given site. You can also check your own website’s page rank. The higher the page rank, the more likely it is that your SEO efforts are succeeding.
What seems to be happening is that the toolbar looks at the URL of the page the browser is displaying and strips off everything down the last “/” (i.e. it goes to the “parent” page in URL terms). If Google has a Toolbar PR for that parent then it subtracts 1 and shows that as the Toolbar PR for this page. If there’s no PR for the parent it goes to the parent’s parent’s page, but subtracting 2, and so on all the way up to the root of your site.  If it can’t find a Toolbar PR to display in this way, that is if it doesn’t find a page with a real calculated PR, then the bar is greyed out.

One of the earliest adopters of Internet marketing in the world of Fortune 500 companies was the Coca-Cola Corporation. Today, this huge purveyor of soft drinks has one of the strongest online portfolios in the world. More than 12,000 websites link to the Coca-Cola homepage, which itself is a stunning display of Internet savvy. Their homepage alone sports an auto-updating social network column, an embedded video, a unique piece of advertising art, frequently rotating copy, an opt-in user registration tab, tie-in branding with pop culture properties, and even a link to the company's career opportunities page. Despite how busy that sounds, the Coca-Cola homepage is clean and easy to read. It is a triumph of Internet marketing for its confidence, personality, and professionalism.

I think it is important you distinguish your advice about no-following INTERNAL links and no-following EXTERNAL links for user-generated content. Most popular UGC-heavy sites have no-followed links as they can’t possibly police them editorially & want to give some indication to the search engines that the links haven’t been editorially approved, but still might provide some user benefit.
As Google becomes more and more sophisticated, one of the major cores of their algorithm, the one dealing with links (called Penguin) aims to value natural, quality links and devalue those unnatural or spammy ones. As a search engine, if they are to stay viable, they have to make sure their results are as honest and high-quality as possible, and that webmasters can't manipulate those results to their own benefit.
If you want to concentrate the PR into one, or a few, pages then hierarchical linking will do that. If you want to average out the PR amongst the pages then "fully meshing" the site (lots of evenly distributed links) will do that - examples 5, 6, and 7 in my above. (NB. this is where Ridings’ goes wrong, in his MiniRank model feedback loops will increase PR - indefinitely!)
Now, how much weight does PageRank carry? Like most every other part of the algorithm, it’s questionable. If we listed all the ranking factors, I don’t suspect it would be in the top 5, but it’s important to remember that the key to ranking well is to be the LESS IMPERFECT than your competition. IE: To have more of the right things that send the right signals in the right places so that Google sees you as a better, more relevant, candidate for the top three on page one. If you and your competitor both have optimized (on-page and technically) for the same keyword phrase perfectly, PR could be the deal breaker that pushes your blue link an inch up.
Google will index this link and see that ESPN has a high authority, and there is a lot of trust in that website, but the relevancy is fairly low. After all, you are a local plumber and they are the biggest sports news website in the world. Once it has indexed your website, it can see that they do not have a lot in common. Now, Google will definitely give you credit for the link, but there is no telling how much.

Mathematical PageRanks for a simple network, expressed as percentages. (Google uses a logarithmic scale.) Page C has a higher PageRank than Page E, even though there are fewer links to C; the one link to C comes from an important page and hence is of high value. If web surfers who start on a random page have an 85% likelihood of choosing a random link from the page they are currently visiting, and a 15% likelihood of jumping to a page chosen at random from the entire web, they will reach Page E 8.1% of the time. (The 15% likelihood of jumping to an arbitrary page corresponds to a damping factor of 85%.) Without damping, all web surfers would eventually end up on Pages A, B, or C, and all other pages would have PageRank zero. In the presence of damping, Page A effectively links to all pages in the web, even though it has no outgoing links of its own.
There's a lot to learn when it comes to the internet marketing field in general, and the digital ether of the web is a crowded space filled with one know-it-all after another that wants to sell you the dream. However, what many people fail to do at the start, and something that Sharpe learned along the way, is to actually understand what's going on out there in the digital world and how businesses and e-commerce works in general, before diving in headfirst.
Suppose instead that page B had a link to pages C and A, page C had a link to page A, and page D had links to all three pages. Thus, upon the first iteration, page B would transfer half of its existing value, or 0.125, to page A and the other half, or 0.125, to page C. Page C would transfer all of its existing value, 0.25, to the only page it links to, A. Since D had three outbound links, it would transfer one third of its existing value, or approximately 0.083, to A. At the completion of this iteration, page A will have a PageRank of approximately 0.458.
PageRank was once available for the verified site maintainers through the Google Webmaster Tools interface. However, on October 15, 2009, a Google employee confirmed that the company had removed PageRank from its Webmaster Tools section, saying that "We've been telling people for a long time that they shouldn't focus on PageRank so much. Many site owners seem to think it's the most important metric for them to track, which is simply not true."[67] In addition, The PageRank indicator is not available in Google's own Chrome browser.
If you’re Matt Cutts and a billion people link to you because you’re the Spam guy at Google, writing great content is enough. For the rest of us in hypercompetitive markets, good content alone is not enough. There was nothing wrong with sculpting page rank to pages on your site that make you money as a means of boosting traffic to those pages. It’s not manipulating Google, there’s more than enough of that going on in the first page of results for most competitive keywords. Geez Matt, give the little guy a break!
Going into network marketing? Understand that if you're not close to the top of the food chain there, your ability to generate any serious amount of income will be limited. Be wary of the hype and the sales pitches that get you thinking that it's going to work the other way. Simply understand that you're going to have to work hard no matter what you pick to do. Email marketing? Sure. You can do that. But you'll need a massive and very targeted list to make any dent.

Ok, everyone been infering from Matt’s comments that all of these nofollow comments would kill the page rank of this post. Which means this page should have shown up on page 1 for the phrase I searched which was “does google follow nofollow”. In spite of all these nofollow comment links it still was presented as the most relevant page, which it probably is.
Check your robots.txt file. Make sure you learn how to hide content you don’t want indexed from search engines and that search engines can find the content you do want indexed, too. (You will want to hide things such as repeat content, which can be penalized by search engines but is still necessary on your site). You’ll find a link to how to modify the robots.txt at the end of this article.
With focus I mean making sure that your pages focus on the same keyword everywhere, and your site focuses on the same high level keywords and sections in your site focusing on their own high level (but not as high as the keywords for which you want your home page to rank) keywords. Focus few people really understand while the interesting thing is that you do this almost automatically right if you do your site architecture and understanding your customers, right.

Online marketing, also called digital marketing, is the process of using the web and internet-connected services to promote your business and website. There are a number of disciplines within online marketing. Some of these include social media, search engine marketing (SEM), search engine optimization (SEO), email marketing, online advertising and mobile advertising.

Denver Search Engine Optimization

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