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.
I have not at all seen the results I would expect in terms of page rank throughout my site. I have almost everything pointing at my home page, with a variety of anchor text, but my rank is 1. There is a page on my site with 3, though, and a couple with 2, so it certainly is not all about links; I do try to have somewhat unique and interesting content, but some of my strong pages are default page content. I will explore the help forum. (I guess these comments are nofollow :P) I would not mind a piece of this page rank …
He is the co-founder of Neil Patel Digital. The Wall Street Journal calls him a top influencer on the web, Forbes says he is one of the top 10 marketers, and Entrepreneur Magazine says he created one of the 100 most brilliant companies. Neil is a New York Times bestselling author and was recognized as a top 100 entrepreneur under the age of 30 by President Obama and a top 100 entrepreneur under the age of 35 by the United Nations. 

Positioning of a webpage on Google SERPs for a keyword depends on relevance and reputation, also known as authority and popularity. PageRank is Google's indication of its assessment of the reputation of a webpage: It is non-keyword specific. Google uses a combination of webpage and website authority to determine the overall authority of a webpage competing for a keyword.[36] The PageRank of the HomePage of a website is the best indication Google offers for website authority.[37]
The leading search engines, such as Google, Bing and Yahoo!, use crawlers to find pages for their algorithmic search results. Pages that are linked from other search engine indexed pages do not need to be submitted because they are found automatically. The Yahoo! Directory and DMOZ, two major directories which closed in 2014 and 2017 respectively, both required manual submission and human editorial review.[39] Google offers Google Search Console, for which an XML Sitemap feed can be created and submitted for free to ensure that all pages are found, especially pages that are not discoverable by automatically following links[40] in addition to their URL submission console.[41] Yahoo! formerly operated a paid submission service that guaranteed crawling for a cost per click;[42] however, this practice was discontinued in 2009.

Having a ‘keyword rich’ domain name may lead to closer scrutiny from Google. According to Moz, Google has “de-prioritized sites with keyword-rich domains that aren’t otherwise high-quality. Having a keyword in your domain can still be beneficial, but it can also lead to closer scrutiny and a possible negative ranking effect from search engines—so tread carefully.”
“Google itself solely decides how much PageRank will flow to each and every link on a particular page. In general, the more links on a page, the less PageRank each link gets. Google might decide some links don’t deserve credit and give them no PageRank. The use of nofollow doesn’t ‘conserve’ PageRank for other links; it simply prevents those links from getting any PageRank that Google otherwise might have given them.”

Now, back to that webmaster: When reaching out, be friendly and introduce yourself. Tell this individual that he or she is linking to some resources that are no longer available. Always provide the exact location of the broken links, so they can be easily found. Give some alternatives to replace those links, including your own website. Try to be helpful, not greedy to get a backlink. Often, this method will work, but there will be cases when the webmaster will refuse to link back to you.

So, the probability for the random surfer reaching one page is the sum of probabilities for the random surfer following links to this page. Now, this probability is reduced by the damping factor d. The justification within the Random Surfer Model, therefore, is that the surfer does not click on an infinite number of links, but gets bored sometimes and jumps to another page at random.
We begin by gaining a sound understanding of your industry, business goals, and target audience. We follow a very formal marketing process for each social media strategy which includes in-depth discovery, market research, project planning, exceptional project management, training, consulting, and reporting. We also incorporate social media ads such as Facebook advertising into many marketing campaigns. As a top digital marketing agency we make social media recommendations that will be best for your business and offer the most engaging experience for your audience.

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