How to use Alexa.com in a proper way in your website promotion??

Is it so popular? So helpful? Do I need to take some action to get a higher points there or it’s indexes are objective?

How do they form “Related links for” section?

Is it important that lots of rival web sites are matched there?

What should I do to be placed in more “Related links for” sections?
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I don't think Alexa is necessarily a good barometer of website popularity. It tracks users who have its toolbar installed, which generally tends to skew in the webmaster community. It is also possible to artificially inflate your Alexa rankings which imo makes it even less relevant.

Thank’s Div,

I understood that Alexa’s rankings have no influence on my PR for example or smth. like that.

That’s a quite powerful engine.. for what ? Do they compete with Google? How can I use it to my benefit?

I still don’t have any clear idea, using Alexa’s rankings before cooperation with some resource I can be well-informed about it’s traffic, it’s owners, it’s rivals? Is that’s all I can do?

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Alexa use Google search engine to provide search results. So better go to google.