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I found hostingdiscussion from Google so I guess it should have high rank, but my rank bar shows that hostingdiscussion has 0/10 rank in google and 51,129 in Alexa.

It seems Google rank is not as important as before.

I also checked your website ranking in Google Toolbar and also verified with some other tools which are also showing that you have PR 4 for your website which URL you mentioned into the post. I think Google Toolbar is most relevant and accurate which tells people about their Google Page Rank which is basically a numeric value assigned by the Google out of 10. From my observation i found that your website had Page Rank 4 which shows the website reputation and quality on the web.

Google rank is important. You will get a higher page rank depending on how many sites are linked to yours. The more site linking to any of your page, the higher your page rank will be.

Google SERP rank is different from Google page rank. All the website ranked on top of search results need not have high PR. The page rank depends on number backlinks for a site. SERP is determined on the relevance of the page for particular search term by Google Algorithm.

You can used the advantage of link building strategy such as blog commenting and forum posting which are really good in generating traffic and getting backlinks to increase your site ranking.

Page rank is a grading system of Google, which shows the popularity of your website. There are many tools on internet, which calculate the Page rank of your website but Google rank is more trustable then other tools. It shows the the accurate page rank of your website. I have used other tools also but no one provide the accurate ranking as Google rank.

I would like to share that the best way to improve page rank, which you are referring as Google rank, is to do link building. With the help of quality link building your site can easily get higher page rank.

If you want to increase your Google rank then do SEO for your website..
and you will get a good Google rank..

I also agree with this suggestion and i also want to add some more information that your URL is search engine friendly or not, structure of your website, your domain life span, content relevancy, meta tags, social factors such as link, ratings, reviews.

I want to give you a suggestion, Google page rank matters for your site because your page rank shows the trust of Google on your website. Alexa is some thing different and Google page rank is different. We can say that both have no inter relation.